Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > CLIQUE:
Reports tagged with clique:
TR95-001 | 1st January 1995
Amos Beimel, Anna Gal, Michael S. Paterson

#### Lower Bounds for Monotone Span Programs

The model of span programs is a linear algebraic model of
computation. Lower bounds for span programs imply lower bounds for
contact schemes, symmetric branching programs and for formula size.
Monotone span programs correspond also to linear secret-sharing schemes.
We present a new technique for proving lower bounds for ... more >>>

TR95-024 | 23rd May 1995
Mihir Bellare, Oded Goldreich, Madhu Sudan

#### Free bits, PCP and Non-Approximability - Towards tight results

Revisions: 4

This paper continues the investigation of the connection between proof
systems and approximation. The emphasis is on proving tight''
non-approximability results via consideration of measures like the
free bit complexity'' and the amortized free bit complexity'' of
proof systems.

The first part of the paper presents a collection of new ... more >>>

TR05-100 | 30th August 2005
David Zuckerman

#### Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number

A randomness extractor is an algorithm which extracts randomness from a low-quality random source, using some additional truly random bits. We construct new extractors which require only log n + O(1) additional random bits for sources with constant entropy rate. We further construct dispersers, which are similar to one-sided extractors, ... more >>>

TR15-013 | 28th January 2015
Subhash Khot, Igor Shinkar

#### On Hardness of Approximating the Parameterized Clique Problem

In the $Gap-clique(k, \frac{k}{2})$ problem, the input is an $n$-vertex graph $G$, and the goal is to decide whether $G$ contains a clique of size $k$ or contains no clique of size $\frac{k}{2}$. It is an open question in the study of fixed parameterized tractability whether the $Gap-clique(k, \frac{k}{2})$ problem ... more >>>

TR15-053 | 7th April 2015
Massimo Lauria, Jakob Nordström

#### Tight Size-Degree Bounds for Sums-of-Squares Proofs

We exhibit families of 4-CNF formulas over n variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) d but require SOS proofs of size n^{Omega(d)} for values of d = d(n) from constant all the way up to n^{delta} for some universal constant delta. This shows that ... more >>>

TR15-157 | 1st September 2015
Thomas O'Neil

#### Representation-Independent Fixed Parameter Tractability for Vertex Cover and Weighted Monotone Satisfiability

A symmetric representation for a set of objects requires the same amount of space for the set as for its complement. Complexity classifications that are based on the length of the input can depend on whether the representation is symmetric. In this article we describe a symmetric representation scheme for ... more >>>

TR15-158 | 27th September 2015
Ofer Grossman, Dana Moshkovitz

#### Amplification and Derandomization Without Slowdown

We present techniques for decreasing the error probability of randomized algorithms and for converting randomized algorithms to deterministic (non-uniform) algorithms. Unlike most existing techniques that involve repetition of the randomized algorithm, and hence a slowdown, our techniques produce algorithms with a similar run-time to the original randomized algorithms.

The ... more >>>

TR18-046 | 9th March 2018
Oded Goldreich, Guy Rothblum

#### Counting $t$-cliques: Worst-case to average-case reductions and Direct interactive proof systems

Revisions: 2

We present two main results regarding the complexity of counting the number of $t$-cliques in a graph.

\begin{enumerate}
\item{\em A worst-case to average-case reduction}:
We reduce counting $t$-cliques in any $n$-vertex graph to counting $t$-cliques in typical $n$-vertex graphs that are drawn from a simple distribution of min-entropy ${\widetilde\Omega}(n^2)$. For ... more >>>

TR21-170 | 25th November 2021
Reyad Abed Elrazik, Robert Robere, Assaf Schuster, Gal Yehuda

#### Pseudorandom Self-Reductions for NP-Complete Problems

A language $L$ is random-self-reducible if deciding membership in $L$ can be reduced (in polynomial time) to deciding membership in $L$ for uniformly random instances. It is known that several "number theoretic" languages (such as computing the permanent of a matrix) admit random self-reductions. Feigenbaum and Fortnow showed that NP-complete ... more >>>

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