Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z - Other

TR04-058 | 28th May 2004
John Case, Sanjay Jain, Eric Martin, Arun Sharma, Frank Stephan

Identifying Clusters from Positive Data

The present work studies clustering from an abstract point of view
and investigates its properties in the framework of inductive inference.
Any class $S$ considered is given by a numbering
$A_0,A_1,...$ of nonempty subsets of the natural numbers
or the rational k-dimensional vector space as a hypothesis space.
A clustering ... more >>>

TR15-184 | 21st November 2015
Matthew Anderson, Michael Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk

Identity Testing and Lower Bounds for Read-$k$ Oblivious Algebraic Branching Programs

Read-$k$ oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs).
In this work, we give an exponential lower bound of $\exp(n/k^{O(k)})$ on the width of any read-$k$ oblivious ABP computing some explicit multilinear polynomial $f$ that is computed by a ... more >>>

TR16-193 | 22nd November 2016
Vikraman Arvind, Pushkar Joglekar, Partha Mukhopadhyay, Raja S

Identity Testing for +-Regular Noncommutative Arithmetic Circuits

An efficient randomized polynomial identity test for noncommutative
polynomials given by noncommutative arithmetic circuits remains an
open problem. The main bottleneck to applying known techniques is that
a noncommutative circuit of size $s$ can compute a polynomial of
degree exponential in $s$ with a double-exponential number of nonzero
monomials. ... more >>>

TR16-009 | 28th January 2016
Rohit Gurjar, Arpita Korwar, Nitin Saxena

Identity Testing for constant-width, and commutative, read-once oblivious ABPs

We give improved hitting-sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known variable order. The best hitting-set known for this case had cost $(nw)^{O(\log n)}$, where $n$ is the number of variables and $w$ is the width of ... more >>>

TR03-055 | 20th July 2003
Jan Krajicek

Implicit proofs

We describe a general method how to construct from
a propositional proof system P a possibly much stronger
proof system iP. The system iP operates with
exponentially long P-proofs described ``implicitly''
by polynomial size circuits.

As an example we prove that proof system iEF, implicit EF,
corresponds to bounded ... more >>>

TR07-028 | 12th February 2007
Daniel Sawitzki

Implicit Simulation of FNC Algorithms

Implicit algorithms work on their input's characteristic functions and should solve problems heuristically by as few and as efficient functional operations as possible. Together with an appropriate data structure to represent the characteristic functions they yield heuristics which are successfully applied in numerous areas. It is known that implicit algorithms ... more >>>

TR00-039 | 25th April 2000
Yevgeniy Dodis

Impossibility of Black-Box Reduction from Non-Adaptively to Adaptively Secure Coin-Flipping

Collective Coin-Flipping is a classical problem where n
computationally unbounded processors are trying to generate a random
bit in a setting where only a single broadcast channel is available
for communication. The protocol is said to be b(n)-resilient if any
adversary that can corrupt up to b(n) players, still cannot ... more >>>

TR11-001 | 2nd January 2011
Scott Aaronson

Impossibility of Succinct Quantum Proofs for Collision-Freeness

We show that any quantum algorithm to decide whether a function $f:\left[n\right] \rightarrow\left[ n\right] $ is a permutation or far from a permutation\ must make $\Omega\left( n^{1/3}/w\right) $ queries to $f$, even if the algorithm is given a $w$-qubit quantum witness in support of $f$ being a permutation. This implies ... more >>>

TR06-110 | 15th August 2006
Nishanth Chandran, Ryan Moriarty, Rafail Ostrovsky, Omkant Pandey, Amit Sahai

Improved Algorithms for Optimal Embeddings

In the last decade, the notion of metric embeddings with
small distortion received wide attention in the literature, with
applications in combinatorial optimization, discrete mathematics, functional
analysis and bio-informatics. The notion of embedding is, given two metric
spaces on the same number of points, to find a bijection that minimizes
more >>>

TR15-112 | 16th July 2015
Ruiwen Chen, Rahul Santhanam

Improved Algorithms for Sparse MAX-SAT and MAX-$k$-CSP

We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-$k$-CSP. For instances with $n$ variables and $cn$ clauses (constraints), we give algorithms running in time $\poly(n)\cdot 2^{n(1-\mu)}$ for
\item $\mu = \Omega(\frac{1}{c} )$ and polynomial space solving MAX-SAT and MAX-$k$-SAT,
\item $\mu = \Omega(\frac{1}{\sqrt{c}} )$ and ... more >>>

TR10-041 | 11th March 2010
Sanjeev Arora, Russell Impagliazzo, William Matthews, David Steurer

Improved Algorithms for Unique Games via Divide and Conquer

We present two new approximation algorithms for Unique Games. The first generalizes the results of Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi who give polynomial time approximation algorithms for graphs with high conductance. We give a polynomial time algorithm assuming only good local conductance, i.e. high conductance for small subgraphs. ... more >>>

TR09-076 | 19th August 2009
Christian Glaßer, Christian Reitwießner, Maximilian Witek

Improved and Derandomized Approximations for Two-Criteria Metric Traveling Salesman

Revisions: 1

We improve and derandomize the best known approximation algorithm for the two-criteria metric traveling salesman problem (2-TSP). More precisely, we construct a deterministic 2-approximation which answers an open question by Manthey.

Moreover, we show that 2-TSP is randomized $(3/2+\epsilon ,2)$-approximable, and we give the first randomized approximations for the two-criteria ... more >>>

TR07-120 | 5th October 2007
Sharon Feldman, Guy Kortsarz, Zeev Nutov

Improved approximation algorithms for directed Steiner forest

We consider the k-Directed Steiner Forest} (k-dsf) problem:
given a directed graph G=(V,E) with edge costs, a collection D subseteq V \times V
of ordered node pairs, and an integer k leq |D|, find a minimum cost subgraph
H of G
that contains an st-path for (at least) k ... more >>>

TR03-008 | 11th February 2003
Piotr Berman, Marek Karpinski

Improved Approximation Lower Bounds on Small Occurrence Optimization

We improve a number of approximation lower bounds for
bounded occurrence optimization problems like MAX-2SAT,
E2-LIN-2, Maximum Independent Set and Maximum-3D-Matching.

more >>>

TR00-021 | 19th April 2000
Uriel Feige, Marek Karpinski, Michael Langberg

Improved Approximation of MAX-CUT on Graphs of Bounded Degree

We analyze the addition of a simple local improvement step to various known
randomized approximation algorithms.
Let $\alpha \simeq 0.87856$ denote the best approximation ratio currently
known for the Max Cut problem on general graphs~\cite{GW95}.
We consider a semidefinite relaxation of the Max Cut problem,
round it using the ... more >>>

TR01-097 | 11th December 2001
Piotr Berman, Marek Karpinski

Improved Approximations for General Minimum Cost Scheduling

We give improved trade-off results on approximating general
minimum cost scheduling problems.

more >>>

TR13-058 | 5th April 2013
Ilan Komargodski, Ran Raz, Avishay Tal

Improved Average-Case Lower Bounds for DeMorgan Formula Size

Revisions: 2

We give a function $h:\{0,1\}^n\to\{0,1\}$ such that every deMorgan formula of size $n^{3-o(1)}/r^2$ agrees with $h$ on at most a fraction of $\frac{1}{2}+2^{-\Omega(r)}$ of the inputs. This improves the previous average-case lower bound of Komargodski and Raz (STOC, 2013).

Our technical contributions include a theorem that shows that the ``expected ... more >>>

TR05-159 | 14th November 2005
Daniel Rolf

Improved Bound for the PPSZ/Schöning-Algorithm for $3$-SAT

The PPSZ Algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable $3$-SAT formula can be found in expected running time at most $O(1.3071^n)$. Its bound degenerates when the number of solutions increases. In 1999, Schöning proved ... more >>>

TR10-192 | 8th December 2010
Frederic Magniez, Ashwin Nayak, Miklos Santha, David Xiao

Improved bounds for the randomized decision tree complexity of recursive majority

Revisions: 1

We consider the randomized decision tree complexity of the recursive 3-majority function. For evaluating a height $h$ formulae, we prove a lower bound for the $\delta$-two-sided-error randomized decision tree complexity of $(1-2\delta)(5/2)^h$, improving the lower bound of $(1-2\delta)(7/3)^h$ given by Jayram et al. (STOC '03). We also state a conjecture ... more >>>

TR16-191 | 24th November 2016
Roei Tell

Improved Bounds for Quantified Derandomization of Constant-Depth Circuits and Polynomials

Revisions: 2

Goldreich and Wigderson (STOC 2014) initiated a study of quantified derandomization, which is a relaxed derandomization problem: For a circuit class $\mathcal{C}$ and a parameter $B=B(n)$, the problem is to decide whether a circuit $C\in\mathcal{C}$ rejects all of its inputs, or accepts all but $B(n)$ of its inputs.

In ... more >>>

TR16-075 | 9th May 2016
Mark Bun, Justin Thaler

Improved Bounds on the Sign-Rank of AC$^0$

Revisions: 1

The sign-rank of a matrix $A$ with entries in $\{-1, +1\}$ is the least rank of a real matrix $B$ with $A_{ij} \cdot B_{ij} > 0$ for all $i, j$. Razborov and Sherstov (2008) gave the first exponential lower bounds on the sign-rank of a function in AC$^0$, answering an ... more >>>

TR16-073 | 7th May 2016
Eli Ben-Sasson, iddo Ben-Tov, Ariel Gabizon, Michael Riabzev

Improved concrete efficiency and security analysis of Reed-Solomon PCPPs

Revisions: 1 , Comments: 1

A Probabilistically Checkable Proof of Proximity (PCPP) for a linear code $C$, enables to determine very efficiently if a long input $x$, given as an oracle, belongs to $C$ or is far from $C$.
PCPPs are often a central component of constructions of Probabilistically Checkable Proofs (PCP)s [Babai et al. ... more >>>

TR10-190 | 9th December 2010
Xin Li

Improved Constructions of Three Source Extractors

We study the problem of constructing extractors for independent weak random sources. The probabilistic method shows that there exists an extractor for two independent weak random sources on $n$ bits with only logarithmic min-entropy. However, previously the best known explicit two source extractor only achieves min-entropy $0.499n$ \cite{Bourgain05}, and the ... more >>>

TR15-125 | 5th August 2015
Xin Li

Improved Constructions of Two-Source Extractors

Revisions: 2

In a recent breakthrough \cite{CZ15}, Chattopadhyay and Zuckerman gave an explicit two-source extractor for min-entropy $k \geq \log^C n$ for some large enough constant $C$. However, their extractor only outputs one bit. In this paper, we improve the output of the two-source extractor to $k^{\Omega(1)}$, while the error remains $n^{-\Omega(1)}$.

... more >>>

TR18-091 | 4th May 2018
Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf, Mary Wootters

Improved decoding of Folded Reed-Solomon and Multiplicity Codes

In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent advances in coding theory. Folded Reed-Solomon codes were the first explicit constructions ... more >>>

TR98-043 | 27th July 1998
Venkatesan Guruswami, Madhu Sudan

Improved decoding of Reed-Solomon and algebraic-geometric codes.

We present an improved list decoding algorithm for decoding
Reed-Solomon codes. Given an arbitrary string of length n, the
list decoding problem is that of finding all codewords within a
specified Hamming distance from the input string.

It is well-known that this decoding problem for Reed-Solomon
codes reduces to the ... more >>>

TR10-080 | 5th May 2010
Andrew Drucker

Improved Direct Product Theorems for Randomized Query Complexity

Revisions: 1

The direct product problem is a fundamental question in complexity theory which seeks to understand how the difficulty of computing a function on each of $k$ independent inputs scales with $k$.
We prove the following direct product theorem (DPT) for query complexity: if every $T$-query algorithm
has success probability at ... more >>>

TR18-110 | 4th June 2018
Fu Li, David Zuckerman

Improved Extractors for Recognizable and Algebraic Sources

We study the task of seedless randomness extraction from recognizable sources, which are uniform distributions over sets of the form {x : f(x) = v} for functions f in some specified class C. We give two simple methods for constructing seedless extractors for C-recognizable sources.
Our first method shows that ... more >>>

TR13-076 | 15th May 2013
Divesh Aggarwal, Chandan Dubey

Improved hardness results for unique shortest vector problem

Revisions: 1

We give several improvements on the known hardness of the unique shortest vector problem in lattices, i.e., the problem of finding a shortest vector in a given lattice given a promise that the shortest vector is unique upto a uniqueness factor $\gamma$.
We give a deterministic reduction from the ... more >>>

TR09-107 | 28th October 2009
Kevin Dick, Chris Umans

Improved inapproximability factors for some $\Sigma_2^p$ minimization problems

We give improved inapproximability results for some minimization problems in the second level of the Polynomial-Time Hierarchy. Extending previous work by Umans [Uma99], we show that several variants of DNF minimization are $\Sigma_2^p$-hard to approximate to within factors of $n^{1/3-\epsilon}$ and $n^{1/2-\epsilon}$ (where the previous results achieved $n^{1/4 - \epsilon}$), ... more >>>

TR09-099 | 16th October 2009
Venkatesan Guruswami, Ali Kemal Sinop

Improved Inapproximability Results for Maximum k-Colorable Subgraph

Revisions: 1

We study the maximization version of the fundamental graph coloring problem. Here the goal is to color the vertices of a $k$-colorable graph with $k$ colors so that a maximum fraction of edges are properly colored (i.e., their endpoints receive different colors). A random $k$-coloring properly colors an expected fraction ... more >>>

TR97-003 | 29th January 1997
Sanjeev Arora, Madhu Sudan

Improved low-degree testing and its applications

NP = PCP(log n, 1) and related results crucially depend upon
the close connection between the probability with which a
function passes a ``low degree test'' and the distance of
this function to the nearest degree d polynomial. In this
paper we study a test ... more >>>

TR06-017 | 12th January 2006
Toshiya Itoh

Improved Lower Bounds for Families of $\varepsilon$-Approximate k$-Restricted Min-Wise Independent Permutations

A family ${\cal F}$ of min-wise independent permutations is known to be a useful tool of indexing replicated documents on the Web. For any integer $n>0$, let $S_{n}$ be the family of al permutations on $[1,n]=\{1,2,\ldots, n\}$.
For any integer $k \in [1,n]$ and any real $\varepsilon >0$, we ... more >>>

TR07-010 | 4th January 2007
Arist Kojevnikov

Improved Lower Bounds for Resolution over Linear Inequalities

Revisions: 1

We continue a study initiated by Krajicek of
a Resolution-like proof system working with clauses of linear
inequalities, R(CP). For all proof systems of this kind
Krajicek proved an exponential lower bound that depends
on the maximal absolute value of coefficients in the given proof and
the maximal clause width.

... more >>>

TR11-156 | 23rd November 2011
Marek Karpinski, Richard Schmied

Improved Lower Bounds for the Shortest Superstring and Related Problems

Revisions: 1

We study the approximation hardness of the Shortest Superstring, the Maximal Compression and
the Maximum Asymmetric Traveling Salesperson (MAX-ATSP) problem.
We introduce a new reduction method that produces strongly restricted instances of
the Shortest Superstring problem, in which the maximal orbit size is eight
(with no ... more >>>

TR14-123 | 7th October 2014
Shachar Lovett, Jiapeng Zhang

Improved noisy population recovery, and reverse Bonami-Beckner inequality for sparse functions

The noisy population recovery problem is a basic statistical inference problem. Given an unknown distribution in $\{0,1\}^n$ with support of size $k$,
and given access only to noisy samples from it, where each bit is flipped independently with probability $1/2-\eps$,
estimate the original probability up to an additive error of ... more >>>

TR96-016 | 6th February 1996
Andrea E. F. Clementi, Luca Trevisan

Improved Non-approximability Results for Minimum Vertex Cover with Density Constraints

We provide new non-approximability results for the restrictions
of the min-VC problem to bounded-degree, sparse and dense graphs.
We show that for a sufficiently large B, the recent 16/15 lower
bound proved by Bellare et al. extends with negligible
loss to graphs with bounded ... more >>>

TR16-115 | 30th July 2016
Xin Li

Improved Non-Malleable Extractors, Non-Malleable Codes and Independent Source Extractors

In this paper we give improved constructions of several central objects in the literature of randomness extraction and tamper-resilient cryptography. Our main results are:

(1) An explicit seeded non-malleable extractor with error $\epsilon$ and seed length $d=O(\log n)+O(\log(1/\epsilon)\log \log (1/\epsilon))$, that supports min-entropy $k=\Omega(d)$ and outputs $\Omega(k)$ bits. Combined with ... more >>>

TR95-053 | 15th October 1995
Petr Slavik

Improved Performance of the Greedy Algorithm for the Minimum Set Cover and Minimum Partial Cover Problems

We establish significantly improved bounds on the performance of the greedy
algorithm for approximating MINIMUM SET COVER and MINIMUM PARTIAL COVER. Our
improvements result from a new approach to both problems. In particular,
(a) we improve the known bound on the performance ratio of the greedy ... more >>>

TR09-141 | 19th December 2009
Anindya De, Omid Etesami, Luca Trevisan, Madhur Tulsiani

Improved Pseudorandom Generators for Depth 2 Circuits

We prove the existence of a $poly(n,m)$-time computable
pseudorandom generator which ``$1/poly(n,m)$-fools'' DNFs with $n$ variables
and $m$ terms, and has seed length $O(\log^2 nm \cdot \log\log nm)$.
Previously, the best pseudorandom generator for depth-2 circuits had seed
length $O(\log^3 nm)$, and was due to Bazzi (FOCS 2007).

It ... more >>>

TR17-171 | 6th November 2017
Eshan Chattopadhyay, Pooya Hatami, Omer Reingold, Avishay Tal

Improved Pseudorandomness for Unordered Branching Programs through Local Monotonicity

Revisions: 1

We present an explicit pseudorandom generator with seed length $\tilde{O}((\log n)^{w+1})$ for read-once, oblivious, width $w$ branching programs that can read their input bits in any order. This improves upon the work of Impaggliazzo, Meka and Zuckerman (FOCS'12) where they required seed length $n^{1/2+o(1)}$.

A central ingredient in our work ... more >>>

TR12-138 | 2nd November 2012
Zeev Dvir, Shubhangi Saraf, Avi Wigderson

Improved rank bounds for design matrices and a new proof of Kelly's theorem

We study the rank of complex sparse matrices in which the supports of different columns have small intersections. The rank of these matrices, called design matrices, was the focus of a recent work by Barak et. al. (BDWY11) in which they were used to answer questions regarding point configurations. In ... more >>>

TR01-055 | 26th July 2001
Alexander Razborov

Improved Resolution Lower Bounds for the Weak Pigeonhole Principle

Recently, Raz established exponential lower bounds on the size
of resolution proofs of the weak pigeonhole principle. We give another
proof of this result which leads to better numerical bounds. Specifically,
we show that every resolution proof of $PHP^m_n$ must have size
$\exp\of{\Omega(n/\log m)^{1/2}}$ which implies an
$\exp\of{\Omega(n^{1/3})}$ bound when ... more >>>

TR11-110 | 10th August 2011
Alessandro Chiesa, Michael Forbes

Improved Soundness for QMA with Multiple Provers

Revisions: 1

We present three contributions to the understanding of QMA with multiple provers:

1) We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap $\Omega(N^{-2})$, which is the best-known soundness gap for two-prover QMA protocols with logarithmic proof size. Maybe ... more >>>

TR99-017 | 4th June 1999
Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, Alex Samorodnitsky

Improved Testing Algorithms for Monotonicity.

Revisions: 1

We present improved algorithms for testing monotonicity of functions.
Namely, given the ability to query an unknown function $f$, where
$\Sigma$ and $\Xi$ are finite ordered sets, the test always accepts a
monotone $f$, and rejects $f$ with high probability if it is $\e$-far
from being monotone (i.e., every ... more >>>

TR03-053 | 8th July 2003
Kazuo Iwama, Suguru Tamaki

Improved Upper Bounds for 3-SAT

This paper presents a new upper bound for the
$k$-satisfiability problem. For small $k$'s, especially for $k=3$,
there have been a lot of algorithms which run significantly faster
than the trivial $2^n$ bound. The following list summarizes those
algorithms where a constant $c$ means that the algorithm runs in time
more >>>

TR03-010 | 13th February 2003
Sven Baumer, Rainer Schuler

Improving a probabilistic 3-SAT Algorithm by Dynamic Search and Independent Clause Pairs

The satisfiability problem of Boolean Formulae in 3-CNF (3-SAT)
is a well known NP-complete problem and the development of faster
(moderately exponential time) algorithms has received much interest
in recent years. We show that the 3-SAT problem can be solved by a
probabilistic algorithm in expected time O(1,3290^n).
more >>>

TR06-078 | 12th June 2006
Tobias Riege, Jörg Rothe

Improving Deterministic and Randomized Exponential-Time Algorithms for the Satisfiability, the Colorability, and the Domatic Number Problem

Revisions: 1

NP-complete problems cannot have efficient algorithms unless P = NP. Due to their importance in practice, however, it is useful to improve the known exponential-time algorithms for NP-complete problems. We survey some of the recent results on such improved exponential-time algorithms for the NP-complete problems satisfiability, graph colorability, and the ... more >>>

TR11-167 | 6th December 2011
Nikolay Vereshchagin

Improving on Gutfreund, Shaltiel, and Ta-Shma's paper "If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances''

Revisions: 1

Assume that $NP\ne RP$. Gutfreund, Shaltiel, and Ta-Shma in [Computational Complexity 16(4):412-441 (2007)] have proved that for every randomized polynomial time decision algorithm $D$ for SAT there is a polynomial time samplable distribution such that $D$ errs with probability at least $1/6-\epsilon$ on a random formula chosen with respect to ... more >>>

TR04-069 | 13th August 2004
Eran Rom, Amnon Ta-Shma

Improving the alphabet size in high noise, almost optimal rate list decodable codes

Revisions: 2

In this note we revisit the construction of high noise, almost
optimal rate list decodable code of Guruswami ("Better extractors for better codes?")
Guruswami showed that based on optimal extractors one can build a
$(1-\epsilon,O({1 \over \epsilon}))$ list decodable codes of rate
$\Omega({\epsilon \over {log{1 \over \epsilon}}})$ and alphabet
size ... more >>>

TR10-135 | 24th August 2010
Oded Goldreich

In a World of P=BPP

Revisions: 2

We show that proving results such as BPP=P essentially
necessitate the construction of suitable pseudorandom generators
(i.e., generators that suffice for such derandomization results).
In particular, the main incarnation of this equivalence
refers to the standard notion of uniform derandomization
and to the corresponding pseudorandom generators
(i.e., the standard uniform ... more >>>

TR11-039 | 19th March 2011
Frederic Green, Daniel Kreymer, Emanuele Viola

In Brute-Force Search of Correlation Bounds for Polynomials

We report on some initial results of a brute-force search for determining the maximum correlation between degree-$d$ polynomials modulo $p$ and the $n$-bit mod $q$ function. For various settings of the parameters $n,d,p,$ and $q$, our results indicate that symmetric polynomials yield the maximum correlation. This contrasts with the previously-analyzed ... more >>>

TR09-045 | 20th May 2009
Iftach Haitner, Omer Reingold, Salil Vadhan, Hoeteck Wee

Inaccessible Entropy

We put forth a new computational notion of entropy, which measures the
(in)feasibility of sampling high entropy strings that are consistent
with a given protocol. Specifically, we say that the i'th round of a
protocol (A, B) has _accessible entropy_ at most k, if no
polynomial-time strategy A^* can generate ... more >>>

TR04-065 | 28th July 2004
Luca Trevisan

Inapproximability of Combinatorial Optimization Problems

Revisions: 1

We survey results on the hardness of approximating combinatorial
optimization problems.

more >>>

TR07-113 | 15th November 2007
Matthew Andrews, Julia Chuzhoy, Venkatesan Guruswami, Sanjeev Khanna, Kunal Talwar, Lisa Zhang

Inapproximability of edge-disjoint paths and low congestion routing on undirected graphs

In the undirected Edge-Disjoint Paths problem with Congestion
(EDPwC), we are given an undirected graph with $V$ nodes, a set of
terminal pairs and an integer $c$. The objective is to route as many
terminal pairs as possible, subject to the constraint that at most
$c$ demands can be routed ... more >>>

TR14-006 | 16th January 2014
Venkatesan Guruswami, Euiwoong Lee

Inapproximability of Feedback Vertex Set for Bounded Length Cycles

Revisions: 1

The Feedback Vertex Set problem (FVS), where the goal is to find a small subset of vertices that intersects every cycle in an input directed graph, is among the fundamental problems whose approximability is not well-understood. One can efficiently find an $\widetilde{O}(\log n)$ factor approximation, and while a constant-factor approximation ... more >>>

TR18-037 | 21st February 2018
Vijay Bhattiprolu, Mrinalkanti Ghosh, Venkatesan Guruswami, Euiwoong Lee, Madhur Tulsiani

Inapproximability of Matrix $p \rightarrow q$ Norms

We study the problem of computing the $p\rightarrow q$ norm of a matrix $A \in R^{m \times n}$, defined as \[ \|A\|_{p\rightarrow q} ~:=~ \max_{x \,\in\, R^n \setminus \{0\}} \frac{\|Ax\|_q}{\|x\|_p} \] This problem generalizes the spectral norm of a matrix ($p=q=2$) and the Grothendieck problem ($p=\infty$, $q=1$), and has been ... more >>>

TR13-071 | 8th May 2013
Venkatesan Guruswami, Sushant Sachdeva, Rishi Saket

Inapproximability of Minimum Vertex Cover on $k$-uniform $k$-partite Hypergraphs

We study the problem of computing the minimum vertex cover on $k$-uniform $k$-partite hypergraphs when the $k$-partition is given. On bipartite graphs ($k=2$), the minimum vertex cover can be computed in polynomial time. For $k \ge 3$, this problem is known to be NP-hard. For general $k$, the problem was ... more >>>

TR15-093 | 5th June 2015
Aviad Rubinstein

Inapproximability of Nash Equilibrium

We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions.

As corollaries, we also prove similar inapproximability results for Bayesian Nash equilibrium in a two-player incomplete ... more >>>

TR12-020 | 3rd March 2012
Daniele Micciancio

Inapproximability of the Shortest Vector Problem: Toward a Deterministic Reduction

Revisions: 1

We prove that the Shortest Vector Problem (SVP) on point lattices is NP-hard to approximate for any constant factor under polynomial time reverse unfaithful random reductions. These are probabilistic reductions with one-sided error that produce false negatives with small probability, but are guaranteed not to produce false positives regardless of ... more >>>

TR03-026 | 20th February 2003
Janka Chlebíková, Miroslav Chlebík

Inapproximability results for bounded variants of optimization problems

We study small degree graph problems such as Maximum Independent Set
and Minimum Node Cover and improve approximation lower bounds for
them and for a number of related problems, like Max-B-Set Packing,
Min-B-Set Cover, Max-Matching in B-uniform 2-regular hypergraphs.
For example, we prove NP-hardness factor of 95/94
more >>>

TR02-030 | 3rd June 2002
Lars Engebretsen, Jonas Holmerin, Alexander Russell

Inapproximability Results for Equations over Finite Groups

Revisions: 1

An equation over a finite group G is an expression of form
w_1 w_2...w_k = 1_G, where each w_i is a variable, an inverted
variable, or a constant from G; such an equation is satisfiable
if there is a setting of the variables to values in G ... more >>>

TR06-052 | 15th April 2006
Wenbin Chen, Jiangtao Meng

Inapproximability Results for the Closest Vector Problem with Preprocessing over infty Norm

We show that the Closest Vector
Problem with Preprocessing over infty Norm
is NP-hard to approximate to within a factor of $(\log
n)^{1/2-\epsilon}$. The result is the same as Regev and Rosen' result, but our proof methods are different from theirs. Their
reductions are based on norm embeddings. However, ... more >>>

TR15-113 | 9th July 2015
Amit Chakrabarti, Tony Wirth

Incidence Geometries and the Pass Complexity of Semi-Streaming Set Cover

Set cover, over a universe of size $n$, may be modelled as a
data-streaming problem, where the $m$ sets that comprise the instance
are to be read one by one. A semi-streaming algorithm is allowed only
$O(n \text{ poly}\{\log n, \log m\})$ space to process this ... more >>>

TR06-044 | 24th January 2006
Andreas Björklund, Thore Husfeldt

Inclusion-Exclusion Based Algorithms for Graph Colouring

We present a deterministic algorithm producing the number of
$k$-colourings of a graph on $n$ vertices in time
We also show that the chromatic number can be found by a
polynomial space algorithm running in time $O(2.2461^n)$.
Finally, we present a family of ... more >>>

TR15-051 | 5th April 2015
Benny Applebaum, Sergei Artemenko, Ronen Shaltiel, Guang Yang

Incompressible Functions, Relative-Error Extractors, and the Power of Nondeterminsitic Reductions

Revisions: 2

A circuit $C$ \emph{compresses} a function $f:\{0,1\}^n\rightarrow \{0,1\}^m$ if given an input $x\in \{0,1\}^n$ the circuit $C$ can shrink $x$ to a shorter $\ell$-bit string $x'$ such that later, a computationally-unbounded solver $D$ will be able to compute $f(x)$ based on $x'$. In this paper we study the existence of ... more >>>

TR04-081 | 9th September 2004
Harry Buhrman, Lance Fortnow, Ilan Newman, Nikolay Vereshchagin

Increasing Kolmogorov Complexity

How much do we have to change a string to increase its Kolmogorov complexity. We show that we can
increase the complexity of any non-random string of length n by flipping O(sqrt(n)) bits and some strings
Omega(sqrt(n)) bit flips. For a given m, we also give bounds for ... more >>>

TR05-136 | 14th November 2005
Anna Gal, Michal Koucky, Pierre McKenzie

Incremental branching programs

In this paper we propose the study of a new model of restricted
branching programs which we call incremental branching programs.
This is in line with the program proposed by Cook in 1974 as an
approach for separating the class of problems solvable in logarithmic
space from problems solvable ... more >>>

TR18-042 | 1st March 2018
Stasys Jukna

Incremental versus Non-Incremental Dynamic Programming

Many dynamic programming algorithms for discrete optimization problems are "pure" in that they only use min/max and addition operations in their recursions. Some of them, in particular those for various shortest path problems, are even "incremental" in that one of the inputs to the addition operations is a variable. We ... more >>>

TR00-035 | 6th June 2000
Nikolay Vereshchagin, Mikhail V. Vyugin

Independent minimum length programs to translate between given strings

A string $p$ is called a program to compute $y$ given $x$
if $U(p,x)=y$, where $U$ denotes universal programming language.
Kolmogorov complexity $K(y|x)$ of $y$ relative to $x$
is defined as minimum length of
a program to compute $y$ given $x$.
Let $K(x)$ denote $K(x|\text{empty string})$
(Kolmogorov complexity of $x$) ... more >>>

TR18-061 | 6th April 2018
Aryeh Grinberg, Ronen Shaltiel, Emanuele Viola

Indistinguishability by adaptive procedures with advice, and lower bounds on hardness amplification proofs

Revisions: 4

We study how well can $q$-query decision trees distinguish between the
following two distributions: (i) $R=(R_1,\ldots,R_N)$ that are i.i.d.
variables, (ii) $X=(R|R \in A)$ where $A$ is an event s.t. $\Pr[R \in A] \ge
2^{-a}$. We prove two lemmas:

- Forbidden-set lemma: There exists $B \subseteq [N]$ of
size ... more >>>

TR16-092 | 3rd June 2016
Gilad Asharov, Alon Rosen, Gil Segev

Indistinguishability Obfuscation Does Not Reduce to Structured Languages

Revisions: 1

We prove that indistinguishability obfuscation (iO) and one-way functions do not naturally reduce to any language within $NP \cap coNP$. This is proved within the framework introduced by Asharov and Segev (FOCS '15) that captures the vast majority of techniques that have been used so far in iO-based constructions.

Our ... more >>>

TR07-017 | 18th January 2007
Ashish Rastogi, Richard Cole

Indivisible Markets with Good Approximate EquilibriumPrices

Revisions: 1

This paper considers the tradeoff between divisibility and the hardness of approximating
equilibrium prices. Tight bounds are obtained for smooth Fisher markets that obey a relaxed
weak gross substitutes property (WGS). A smooth market is one in which small changes in
prices cause only proportionately small changes ... more >>>

TR14-019 | 14th February 2014
Parikshit Gopalan, Amir Yehudayoff

Inequalities and tail bounds for elementary symmetric polynomials

This paper studies the elementary symmetric polynomials $S_k(x)$ for $x \in \mathbb{R}^n$. We show that if $|S_k(x)|,|S_{k+1}(x)|$ are small for some $k>0$ then $|S_\ell(x)|$ is also small for all $\ell > k$. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only $t$-wise ... more >>>

TR07-096 | 8th October 2007
Lance Fortnow, Rahul Santhanam

Infeasibility of Instance Compression and Succinct PCPs for NP

We study the notion of "instance compressibility" of NP problems [Harnik-Naor06], closely related to the notion of kernelization in parameterized complexity theory [Downey-Fellows99, Flum-Grohe06, Niedermeier06]. A language $L$ in NP is instance compressible if there
is a polynomial-time computable function $f$ and a set $A$ such that
for each instance ... more >>>

TR06-010 | 1st December 2005
Reka Albert, Bhaskar DasGupta, Riccardo Dondi, Eduardo D. Sontag

Inferring (Biological) Signal Transduction Networks via Transitive Reductions of Directed Graphs

In this paper we consider the p-ary transitive reduction (TR<sub>p</sub>) problem where p>0 is an integer; for p=2 this problem arises in inferring a sparsest possible (biological) signal transduction network consistent with a set of experimental observations with a goal to minimize false positive inferences even if risking false negatives. ... more >>>

TR06-051 | 8th April 2006
Alan Nash, Russell Impagliazzo, Jeff Remmel

Infinitely-Often Universal Languages and Diagonalization

Diagonalization is a powerful technique in recursion theory and in
computational complexity \cite{For00}. The limits of this technique are
not clear. On the one hand, many people argue that conflicting
relativizations mean a complexity question cannot be resolved using only
diagonalization. On the other hand, it is not clear that ... more >>>

TR15-060 | 14th April 2015
Omri Weinstein

Information Complexity and the Quest for Interactive Compression

Revisions: 1

Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open problems in communication complexity and circuit complexity. A notable achievement of information complexity is ... more >>>

TR15-070 | 22nd April 2015
Himanshu Tyagi, Shaileshh Venkatakrishnan , Pramod Viswanath, Shun Watanabe

Information Complexity Density and Simulation of Protocols

Revisions: 1

A simulation of an interactive protocol entails the use of an interactive communication to produce the output of the protocol to within a fixed statistical distance $\epsilon$. Recent works in the TCS community have propagated that the information complexity of the protocol plays a central role in characterizing the minimum ... more >>>

TR14-132 | 23rd October 2014
Diptarka Chakraborty, Elazar Goldenberg, Michal Koucky

Information Complexity for Multiparty Communication

Revisions: 2

In this paper, we have studied the information complexity for the communication model involving more than two parties. A lot of work has already been done on the information complexity in two party communication model and the question of extending the definition of information complexity to the multiparty communication model ... more >>>

TR15-023 | 10th February 2015
Mark Braverman, Jon Schneider

Information complexity is computable

The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary function $f$ to within any additive error $\alpha>0$, thus resolving an ... more >>>

TR10-076 | 18th April 2010
Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, Andrew McGregor

Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition

Revisions: 1

This paper makes three main contributions to the theory of communication complexity and stream computation. First, we present new bounds on the information complexity of AUGMENTED-INDEX. In contrast to analogous results for INDEX by Jain, Radhakrishnan and Sen [J. ACM, 2009], we have to overcome the significant technical challenge that ... more >>>

TR00-016 | 29th February 2000
Mikhail V. Vyugin

Information Distance and Conditional Complexities

C.H.~Bennett, P.~G\'acs, M.~Li, P.M.B.~Vit\'anyi, and W.H.~Zurek
have defined information distance between two strings $x$, $y$
d(x,y)=\max\{ K(x|y), K(y|x) \}
where $K(x|y)$ is the conditional Kolmogorov complexity.
It is easy to see that for any string $x$ and any integer $n$
there is a string $y$ ... more >>>

TR12-177 | 19th December 2012
Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

Information lower bounds via self-reducibility

We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform ... more >>>

TR17-078 | 21st April 2017
Nico Döttling, Jesper Buus Nielsen, Maceij Obremski

Information Theoretic Continuously Non-Malleable Codes in the Constant Split-State Model

Revisions: 1

We present an information-theoretically secure continuously non-malleable code in the constant split-state model, where there is a self-destruct mechanism which ensures that the adversary loses access to tampering after the first failed decoding. Prior to our result only codes with computational security were known for this model, and it has ... more >>>

TR16-078 | 9th May 2016
Gregory Valiant, Paul Valiant

Information Theoretically Secure Databases

We introduce the notion of a database system that is information theoretically "secure in between accesses"--a database system with the properties that 1) users can efficiently access their data, and 2) while a user is not accessing their data, the user's information is information theoretically secure to malicious agents, provided ... more >>>

TR04-068 | 13th August 2004
Nir Ailon, Bernard Chazelle

Information Theory in Property Testing and Monotonicity Testing in Higher Dimension

In general property testing, we are given oracle access to a function $f$, and we wish to randomly test if the function satisfies a given property $P$, or it is $\epsilon$-far from having that property. In a more general setting, the domain on which the function is defined is equipped ... more >>>

TR17-182 | 21st November 2017
Mark Braverman, Young Kun Ko

Information Value of Two-Prover Games

We introduce a generalization of the standard framework for studying the difficulty of two-prover games. Specifically, we study the model where Alice and Bob are allowed to communicate (with information constraints) --- in contrast to the usual two-prover game where they are not allowed to communicate after receiving their respective ... more >>>

TR13-158 | 18th November 2013
Gábor Braun, Rahul Jain, Troy Lee, Sebastian Pokutta

Information-theoretic approximations of the nonnegative rank

Revisions: 3

Common information was introduced by Wyner as a measure of dependence of two
random variables. This measure has been recently resurrected as a lower bound on the logarithm of the nonnegative rank of a nonnegative matrix. Lower bounds on nonnegative rank have important applications to several areas such
as communication ... more >>>

TR01-015 | 9th February 2001
Amos Beimel, Yuval Ishai

Information-Theoretic Private Information Retrieval: A Unified Construction

A Private Information Retrieval (PIR) protocol enables a user to
retrieve a data item from a database while hiding the identity of the
item being retrieved. In a $t$-private, $k$-server PIR protocol the
database is replicated among $k$ servers, and the user's privacy is
protected from any collusion of up ... more >>>

TR15-029 | 18th February 2015
Stanislav Zak

Inherent logic and complexity

Abstract. The old intuitive question "what does the machine think" at
different stages of its computation is examined. Our paper is based on
the formal de nitions and results which are collected in the branching
program theory around the intuitive question "what does the program
know about the contents of ... more >>>

TR17-184 | 29th November 2017
Vladimir Podolskii, Alexander A. Sherstov

Inner Product and Set Disjointness: Beyond Logarithmically Many Parties

A basic goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems $f\colon(\{0,1\}^n)^{k}\to\{0,1\}$ with $k\gg\log n$ parties. We study the problems of inner product and set disjointness and determine their randomized communication complexity for every $k\geq\log n$, showing in both cases that $\Theta(1+\lceil\log n\rceil/\log\lceil1+k/\log n\rceil)$ bits are ... more >>>

TR11-012 | 2nd February 2011
Andrej Bogdanov, Alon Rosen

Input locality and hardness amplification

We establish new hardness amplification results for one-way functions in which each input bit influences only a small number of output bits (a.k.a. input-local functions). Our transformations differ from previous ones in that they approximately preserve input locality and at the same time retain the input size of the original ... more >>>

TR11-023 | 16th February 2011
Oded Goldreich, Or Meir

Input-Oblivious Proof Systems and a Uniform Complexity Perspective on P/poly

Revisions: 5 , Comments: 2

We initiate a study of input-oblivious proof systems, and present a few preliminary results regarding such systems.
Our results offer a perspective on the intersection of the non-uniform complexity class P/poly with uniform complexity classes such as NP and IP.
In particular, we provide a uniform complexity formulation of the ... more >>>

TR09-022 | 16th February 2009
Jack H. Lutz, Elvira Mayordomo

Inseparability and Strong Hypotheses for Disjoint NP Pairs

Revisions: 1

This paper investigates the existence of inseparable disjoint
pairs of NP languages and related strong hypotheses in
computational complexity. Our main theorem says that, if NP does
not have measure 0 in EXP, then there exist disjoint pairs of NP
languages that are P-inseparable, in fact TIME(2^(n^k)-inseparable.
We also relate ... more >>>

TR12-077 | 10th June 2012
Chiranjit Chakraborty, Rahul Santhanam

Instance Compression for the Polynomial Hierarchy and Beyond

Comments: 2

We define instance compressibility for parametric problems in PH and PSPACE. We observe that

the problem \Sigma_{i}CircuitSAT of deciding satisfiability of a quantified Boolean circuit with i-1 alternations of quantifiers starting with an existential uantifier is complete for parametric problems in \Sigma_{i}^{p} with respect to W-reductions, and that analogously ... more >>>

TR13-111 | 17th August 2013
Gregory Valiant, Paul Valiant

Instance-by-instance optimal identity testing

We consider the problem of verifying the identity of a distribution: Given the description of a distribution over a discrete support $p=(p_1,p_2,\ldots,p_n)$, how many samples (independent draws) must one obtain from an unknown distribution, $q$, to distinguish, with high probability, the case that $p=q$ from the case that the total ... more >>>

TR08-068 | 3rd July 2008
Lior Malka

Instance-Dependent Commitment Schemes and the Round Complexity of Perfect Zero-Knowledge Proofs

We study the question whether the number of rounds in public-coin perfect zero-knowledge (PZK) proofs can be collapsed to a constant. Despite extensive research into the round complexity of interactive
and zero-knowledge protocols, there is no indication how to address this question. Furthermore, the main tool to tackle this question ... more >>>

TR00-012 | 14th February 2000
Ke Yang

Integer Circuit Evaluation is PSPACE-complete

In this paper, we address the problem of evaluating the
Integer Circuit (IC), or the $\{\cup, \times, +\}$-circuit over
the set of natural numbers. The problem is a natural extension
to the integer expression by Stockmeyer and Mayer, and is also studied
by Mckenzie, Vollmer and Wagner in ... more >>>

TR13-001 | 2nd January 2013
Gillat Kol, Ran Raz

Interactive Channel Capacity

Revisions: 1

We study the interactive channel capacity of an $\epsilon$-noisy channel. The interactive channel capacity $C(\epsilon)$ is defined as the minimal ratio between the communication complexity of a problem (over a non-noisy channel), and the communication complexity of the same problem over the binary symmetric channel with noise rate $\epsilon$, where ... more >>>

TR17-093 | 22nd May 2017
Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Interactive Coding Over the Noisy Broadcast Channel

A set of $n$ players, each holding a private input bit, communicate over a noisy broadcast channel. Their mutual goal is for all players to learn all inputs. At each round one of the players broadcasts a bit to all the other players, and the bit received by each player ... more >>>

TR18-054 | 24th March 2018
Klim Efremenko, Elad Haramaty, Yael Kalai

Interactive Coding with Constant Round and Communication Blowup

Revisions: 1

The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOCS 1992, STOC 1993). These works show how to convert any two-party interactive protocol into one that is resilient to constant-fraction of error, while blowing up the communication by only a constant factor. Since ... more >>>

TR15-168 | 18th October 2015
Gillat Kol

Interactive Compression for Product Distributions

We study the interactive compression problem: Given a two-party communication protocol with small information cost, can it be compressed so that the total number of bits communicated is also small? We consider the case where the parties have inputs that are independent of each other, and give a simulation protocol ... more >>>

TR11-123 | 15th September 2011
Mark Braverman

Interactive information complexity

The primary goal of this paper is to define and study the interactive information complexity of functions. Let $f(x,y)$ be a function, and suppose Alice is given $x$ and Bob is given $y$. Informally, the interactive information complexity $IC(f)$ of $f$ is the least amount of information Alice and Bob ... more >>>

TR10-020 | 19th February 2010
Vipul Goyal, Yuval Ishai, Mohammad Mahmoody, Amit Sahai

Interactive Locking, Zero-Knowledge PCPs, and Unconditional Cryptography

Motivated by the question of basing cryptographic protocols on stateless tamper-proof hardware tokens, we revisit the question of unconditional two-prover zero-knowledge proofs for $NP$. We show that such protocols exist in the {\em interactive PCP} model of Kalai and Raz (ICALP '08), where one of the provers is replaced by ... more >>>

TR07-031 | 26th March 2007
Yael Tauman Kalai, Ran Raz

Interactive PCP

An interactive-PCP (say, for the membership $x \in L$) is a
proof that can be verified by reading only one of its bits, with the
help of a very short interactive-proof.
We show that for membership in some languages $L$, there are
interactive-PCPs that are significantly shorter than the known
more >>>

TR10-187 | 3rd December 2010
Gus Gutoski

Interactive proofs with competing teams of no-signaling provers

Revisions: 2

This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier to reject. Each team consists of two provers who jointly implement a no-signaling ... more >>>

TR99-024 | 25th June 1999
Oded Goldreich, Silvio Micali.

Interleaved Zero-Knowledge in the Public-Key Model.

Revisions: 1 , Comments: 1

We introduce the notion of Interleaved Zero-Knowledge (iZK),
a new security measure for cryptographic protocols which strengthens
the classical notion of zero-knowledge, in a way suitable for multiple
concurrent executions in an asynchronous environment like the internet.
We prove that iZK protocols are robust: they are ``parallelizable'',
and ... more >>>

TR14-101 | 8th August 2014
Balthazar Bauer, Shay Moran, Amir Yehudayoff

Internal compression of protocols to entropy

Revisions: 1

We study internal compression of communication protocols
to their internal entropy, which is the entropy of the transcript from the players' perspective.
We first show that errorless compression to the internal entropy
(and hence to the internal information) is impossible.
We then provide two internal compression schemes with error.
One ... more >>>

TR97-015 | 21st April 1997
Jan Krajicek

Interpolation by a game

We introduce a notion of a "real game"
(a generalization of the Karchmer - Wigderson game),
and "real communication complexity",
and relate them to the size of monotone real formulas
and circuits. We give an exponential lower bound
for tree-like monotone protocols of small real
communication complexity ... more >>>

TR12-032 | 4th April 2012
Sebastian Kuhnert, Johannes Köbler, Osamu Watanabe

Interval graph representation with given interval and intersection lengths

We consider the problem of finding interval representations of graphs that additionally respect given interval lengths and/or pairwise intersection lengths, which are represented as weight functions on the vertices and edges, respectively. Pe'er and Shamir proved that the problem is NP-complete if only the former are given [SIAM J. Discr. ... more >>>

TR10-043 | 5th March 2010
Johannes Köbler, Sebastian Kuhnert, Bastian Laubner, Oleg Verbitsky

Interval Graphs: Canonical Representation in Logspace

Revisions: 1

We present a logspace algorithm for computing a canonical interval representation and a canonical labeling of interval graphs. As a consequence, the isomorphism and automorphism problems for interval graphs are solvable in logspace.

more >>>

TR10-082 | 11th May 2010
Oded Goldreich

Introduction to Testing Graph Properties

The aim of this article is to introduce the reader to the study
of testing graph properties, while focusing on the main models
and issues involved. No attempt is made to provide a
comprehensive survey of this study, and specific results
are often mentioned merely as illustrations of general ... more >>>

TR10-051 | 26th March 2010
Madhu Sudan

Invariance in Property Testing

Property testing considers the task of testing rapidly (in particular, with very few samples into the data), if some massive data satisfies some given property, or is far from satisfying the property. For ``global properties'', i.e., properties that really depend somewhat on every piece of the data, one could ask ... more >>>

TR07-123 | 21st November 2007
Shachar Lovett, Roy Meshulam, Alex Samorodnitsky

Inverse Conjecture for the Gowers norm is false

Revisions: 2

Let $p$ be a fixed prime number, and $N$ be a large integer.
The 'Inverse Conjecture for the Gowers norm' states that if the "$d$-th Gowers norm" of a function $f:\F_p^N \to \F_p$ is non-negligible, that is larger than a constant independent of $N$, then $f$ can be non-trivially ... more >>>

TR12-152 | 7th November 2012
Anindya De, Ilias Diakonikolas, Rocco Servedio

Inverse Problems in Approximate Uniform Generation

We initiate the study of \emph{inverse} problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform random satisfying assignments of an unknown function $f$ belonging to a class $\C$ of Boolean functions ... more >>>

TR10-121 | 28th July 2010
Ashwin Nayak

Inverting a permutation is as hard as unordered search

Revisions: 1

We describe a reduction from the problem of unordered search(with a unique solution) to the problem of inverting a permutation. Since there is a straightforward reduction in the reverse direction, the problems are essentially equivalent.

The reduction helps us bypass the Bennett-Bernstein-Brassard-Vazirani hybrid argument (1997} and the Ambainis quantum adversary ... more >>>

TR06-024 | 18th February 2006
Harry Burhman, Lance Fortnow, Michal Koucky, John Rogers, Nikolay Vereshchagin

Inverting onto functions might not be hard

The class TFNP, defined by Megiddo and Papadimitriou, consists of
multivalued functions with values that are polynomially verifiable
and guaranteed to exist. Do we have evidence that such functions are
hard, for example, if TFNP is computable in polynomial-time does
this imply the polynomial-time hierarchy collapses?

We give a relativized ... more >>>

TR99-041 | 22nd August 1999
Oliver Kullmann

Investigating a general hierarchy of polynomially decidable classes of CNF's based on short tree-like resolution proofs

Revisions: 2

A relativized hierarchy of conjunctive normal forms
is introduced, recognizable and SAT decidable in polynomial
time. The corresponding hardness parameter, the first level
of inclusion in the hierarchy, is studied in detail, admitting
several characterizations, e.g., using pebble games, the space
complexity of (relativized) tree-like ... more >>>

TR10-137 | 29th August 2010
Or Meir

IP = PSPACE using Error Correcting Codes

Revisions: 5

The IP theorem, which asserts that IP = PSPACE (Lund et. al., and Shamir, in J. ACM 39(4)), is one of the major achievements of complexity theory. The known proofs of the theorem are based on the arithmetization technique, which transforms a quantified Boolean formula into a related polynomial. The ... more >>>

TR17-179 | 20th November 2017
Alexander Knop

IPS-like Proof Systems Based on Binary Decision Diagrams

It is well-known that there is equivalence between ordered resolution and ordered binary decision diagrams (OBDD) [LNNW95]; i.e., for any unsatisfiable formula ?, the size of the smallest ordered resolution refutation of ? equal to the size of the smallest OBDD for the canonical search problem corresponding to ?. But ... more >>>

TR12-084 | 3rd July 2012
Rahul Santhanam

Ironic Complicity: Satisfiability Algorithms and Circuit Lower Bounds

I discuss recent progress in developing and exploiting connections between
SAT algorithms and circuit lower bounds. The centrepiece of the article is
Williams' proof that $NEXP \not \subseteq ACC^0$, which proceeds via a new
algorithm for $ACC^0$-SAT beating brute-force search. His result exploits
a formal connection from non-trivial SAT algorithms ... more >>>

TR17-016 | 31st January 2017
Vishwas Bhargava, Gábor Ivanyos, Rajat Mittal, Nitin Saxena

Irreducibility and deterministic r-th root finding over finite fields

Constructing $r$-th nonresidue over a finite field is a fundamental computational problem. A related problem is to construct an irreducible polynomial of degree $r^e$ (where $r$ is a prime) over a given finite field $\F_q$ of characteristic $p$ (equivalently, constructing the bigger field $\F_{q^{r^e}}$). Both these problems have famous randomized ... more >>>

TR98-003 | 3rd November 1997
I. Cahit, M. Tezer

Irregular Assignments of the Forest of Paths

An irregular assignement of $G$ is labelling $f: E \ra
\{1,2,...,m\}$ of the
edge-set of $G$ such that all of the induced vertex labels computed as
$\sigma_{v\in e}f(e)$ are distinct. The minimal number $m$ for which this
is possible is called the minimal irregularity strength $s_{m}(G)$ of $G$.
The ... more >>>

TR02-053 | 20th July 2002
Lars Engebretsen, Venkatesan Guruswami

Is Constraint Satisfaction Over Two Variables Always Easy?

By the breakthrough work of Håstad, several constraint satisfaction
problems are now known to have the following approximation resistance
property: satisfying more clauses than what picking a random
assignment would achieve is NP-hard. This is the case for example for
Max E3-Sat, Max E3-Lin and Max E4-Set Splitting. A notable ... more >>>

TR11-151 | 9th November 2011
Valentine Kabanets, Osamu Watanabe

Is the Valiant-Vazirani Isolation Lemma Improvable?

Revisions: 2

The Valiant-Vazirani Isolation Lemma [TCS, vol. 47, pp. 85--93, 1986] provides an efficient procedure for isolating a satisfying assignment of a given satisfiable circuit: given a Boolean circuit $C$ on $n$ input variables, the procedure outputs a new circuit $C'$ on the same $n$ input variables with the property that ... more >>>

TR15-146 | 7th September 2015
Elette Boyle, Moni Naor

Is There an Oblivious RAM Lower Bound?

Revisions: 1

An Oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (JACM 1996), is a (probabilistic) RAM that hides its access pattern, i.e. for every input the observed locations accessed are similarly distributed. Great progress has been made in recent years in minimizing the overhead of ORAM constructions, with the goal of ... more >>>

TR17-127 | 12th August 2017
Rohit Gurjar, Thomas Thierauf, Nisheeth Vishnoi

Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces

Revisions: 1

We deterministically construct quasi-polynomial weights in quasi-polynomial time, such that in a given polytope with totally unimodular constraints, one vertex is isolated, i.e., there is a unique minimum weight vertex.
More precisely,
the property that we need is that every face of the polytope lies in an affine space defined ... more >>>

TR16-155 | 10th October 2016
Vaibhav Krishan, Nutan Limaye

Isolation Lemma for Directed Reachability and NL vs. L

In this work we study the problem of efficiently isolating witnesses for the complexity classes NL and LogCFL, which are two well-studied complexity classes contained in P. We prove that if there is a L/poly randomized procedure with success probability at least 2/3 for isolating an s-t path in a ... more >>>

TR10-194 | 9th December 2010
Thanh Minh Hoang

Isolation of Matchings via Chinese Remaindering

In this paper we investigate the question whether a perfect matching can be isolated by a weighting scheme
using Chinese Remainder Theorem (short: CRT). We give a systematical analysis to a method based on CRT
suggested by Agrawal in a CCC'03-paper
for testing perfect matchings. We show that ... more >>>

TR98-019 | 5th April 1998
Eric Allender, Klaus Reinhardt

Isolation, Matching, and Counting

We show that the perfect matching problem is in the
complexity class SPL (in the nonuniform setting).
This provides a better upper bound on the complexity of the
matching problem, as well as providing motivation for studying
the complexity class SPL.

Using similar ... more >>>

TR11-137 | 14th October 2011
Vikraman Arvind, Yadu Vasudev

Isomorphism Testing of Boolean Functions Computable by Constant Depth Circuits

Given two $n$-variable boolean functions $f$ and $g$, we study the problem of computing an $\varepsilon$-approximate isomorphism between them. I.e.\ a permutation $\pi$ of the $n$ variables such that $f(x_1,x_2,\ldots,x_n)$ and $g(x_{\pi(1)},x_{\pi(2)},\ldots,x_{\pi(n)})$ differ on at most an $\varepsilon$ fraction of all boolean inputs $\{0,1\}^n$. We give a randomized $2^{O(\sqrt{n}\log(n)^{O(1)})}$ algorithm ... more >>>

TR14-104 | 9th August 2014
Atri Rudra, Mary Wootters

It'll probably work out: improved list-decoding through random operations

In this work, we introduce a framework to study the effect of random operations on the combinatorial list decodability of a code.
The operations we consider correspond to row and column operations on the matrix obtained from the code by stacking the codewords together as columns. This captures many natural ... more >>>

TR06-123 | 15th September 2006
Venkatesan Guruswami, Venkatesan Guruswami

Iterative Decoding of Low-Density Parity Check Codes (A Survey)

Much progress has been made on decoding algorithms for
error-correcting codes in the last decade. In this article, we give an
introduction to some fundamental results on iterative, message-passing
algorithms for low-density parity check codes. For certain
important stochastic channels, this line of work has enabled getting
very close to ... more >>>

ISSN 1433-8092 | Imprint