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Electronic Colloquium on Computational Complexity

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All reports by Author Osamu Watanabe:

TR19-091 | 7th July 2019
Ryo Ashida, Tatsuya Imai, Kotaro Nakagawa, A. Pavan, Vinodchandran Variyam, Osamu Watanabe

A Sublinear-space and Polynomial-time Separator Algorithm for Planar Graphs

In [12] (CCC 2013), the authors presented an algorithm for the reachability problem over directed planar graphs that runs in polynomial-time and uses $O(n^{1/2+\epsilon})$ space. A critical ingredient of their algorithm is a polynomial-time, $\tldO(\sqrt{n})$-space algorithm to compute a separator of a planar graph. The conference version provided a sketch ... more >>>

TR19-025 | 28th February 2019
Shuichi Hirahara, Osamu Watanabe

On Nonadaptive Reductions to the Set of Random Strings and Its Dense Subsets

We investigate the computational power of an arbitrary distinguisher for (not necessarily computable) hitting set generators as well as the set of Kolmogorov-random strings. This work contributes to (at least) two lines of research. One line of research is the study of the limits of black-box reductions to some distributional ... more >>>

TR17-140 | 11th September 2017
Tong Qin, Osamu Watanabe

An improvement of the algorithm of Hertli for the unique 3SAT problem

We propose a simple idea for improving the randomized algorithm of Hertli for the Unique 3SAT problem.

more >>>

TR15-198 | 30th November 2015
Shuichi Hirahara, Osamu Watanabe

Limits of Minimum Circuit Size Problem as Oracle

Revisions: 1

The Minimum Circuit Size Problem (MCSP) is known to be hard for statistical zero knowledge via a BPP-reduction (Allender and Das, 2014), whereas establishing NP-hardness of MCSP via a polynomial-time many-one reduction is difficult (Murray and Williams, 2015) in the sense that it implies ZPP $\neq$ EXP, which is a ... more >>>

TR14-071 | 7th May 2014
Tetsuo Asano, David Kirkpatrick, Kotaro Nakagawa, Osamu Watanabe

O(sqrt(n))-Space and Polynomial-time Algorithm for the Planar Directed Graph Reachability Problem

We show an O(sqrt(n))-space and polynomial-time algorithm for solving the planar directed graph reachability problem. Imai et al. showed in CCC 2013 that the problem is solvable in O(n^{1/2+eps})-space and polynomial-time by using separators for planar graphs, and it has been open whether the space bound can be improved to ... more >>>

TR13-176 | 8th December 2013
Daniel Kane, Osamu Watanabe

A Short Implicant of CNFs with Relatively Many Satisfying Assignments

Revisions: 1 , Comments: 1

Consider any Boolean function $F(X_1,\ldots,X_N)$ that has more than $2^{-N^{d}}$ satisfying assignments and that can be expressed by a CNF formula with at most $N^{1+e}$ clauses for some $d>0$ and $e>0$ such that $d+e$ is less than $1$ (*). Then how many variables do we need to fix in order ... 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 >>>

TR12-002 | 4th January 2012
Akinori Kawachi, Benjamin Rossman, Osamu Watanabe

Query Complexity and Error Tolerance of Witness Finding Algorithms

Revisions: 3

We propose an abstract framework for studying search-to-decision reductions for NP. Specifically, we study the following witness finding problem: for a hidden nonempty set $W\subseteq\{0,1\}^n$, the goal is to output a witness in $W$ with constant probability by making randomized queries of the form ``is $Q\cap W$ nonempty?''\ where $Q\subseteq\{0,1\}^n$. ... 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 >>>

TR09-023 | 12th March 2009
Akinori Kawachi, Osamu Watanabe

Strong Hardness Preserving Reduction from a P-Samplable Distribution to the Uniform Distribution for NP-Search Problems

Impagliazzo and Levin demonstrated [IL90] that the average-case hardness of any NP-search problem under any P-samplable distribution implies that of another NP-search problem under the uniform distribution. For this they developed a way to define a reduction from an NP-search problem F with ``mild hardness'' under any P-samplable distribution H; ... more >>>

TR09-019 | 10th March 2009
Agrawal Manindra, Osamu Watanabe

One-Way Functions and the Isomorphism Conjecture

We study the Isomorphism Conjecture proposed by Berman and Hartmanis.
It states that all sets complete for NP under polynomial-time many-one
reductions are P-isomorphic to each other. From previous research
it has been widely believed that all NP-complete sets are reducible
each other by one-to-one and length-increasing polynomial-time
reductions, but ... more >>>

TR00-081 | 5th September 2000
Shin Aida, Rainer Schuler, Tatsuie Tsukiji, Osamu Watanabe

On the difference between polynomial-time many-one and truth-table reducibilities on distributional problems

In this paper we separate many-one reducibility from truth-table
reducibility for distributional problems in DistNP under the
hypothesis that P neq NP. As a first example we consider the
3-Satisfiability problem (3SAT) with two different distributions
on 3CNF formulas. We show that 3SAT using a version of the
standard distribution ... more >>>

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