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Electronic Colloquium on Computational Complexity

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Reports tagged with SETH:
TR15-148 | 9th September 2015
Marco Carmosino, Jiawei Gao, Russell Impagliazzo, Ivan Mikhailin, Ramamohan Paturi, Stefan Schneider

Nondeterministic extensions of the Strong Exponential Time Hypothesis and consequences for non-reducibility

Revisions: 1

We introduce the Nondeterministic Strong Exponential Time Hypothesis
(NSETH) as a natural extension of the Strong Exponential Time
Hypothesis (SETH). We show that both refuting and proving
NSETH would have interesting consequences.

In particular we show that disproving NSETH would ... more >>>

TR19-054 | 9th April 2019
Joshua Brakensiek, Venkatesan Guruswami

Bridging between 0/1 and Linear Programming via Random Walks

Under the Strong Exponential Time Hypothesis, an integer linear program with $n$ Boolean-valued variables and $m$ equations cannot be solved in $c^n$ time for any constant $c < 2$. If the domain of the variables is relaxed to $[0,1]$, the associated linear program can of course be solved in polynomial ... more >>>

TR19-159 | 11th November 2019
Noah Stephens-Davidowitz, Vinod Vaikuntanathan

SETH-hardness of Coding Problems

We show that assuming the strong exponential-time hypothesis (SETH), there are no non-trivial algorithms for the nearest codeword problem (NCP), the minimum distance problem (MDP), or the nearest codeword problem with preprocessing (NCPP) on linear codes over any finite field. More precisely, we show that there are no NCP, MDP, ... more >>>

TR19-181 | 9th December 2019
Michal Koucky, Vojtech Rodl, Navid Talebanfard

A Separator Theorem for Hypergraphs and a CSP-SAT Algorithm

Revisions: 1

We show that for every $r \ge 2$ there exists $\epsilon_r > 0$ such that any $r$-uniform hypergraph on $m$ edges with bounded vertex degree has a set of at most $(\frac{1}{2} - \epsilon_r)m$ edges the removal of which breaks the hypergraph into connected components with at most $m/2$ edges. ... more >>>

TR20-011 | 9th February 2020
Dominik Scheder, Navid Talebanfard

Super Strong ETH is true for strong PPSZ

We construct $k$-CNFs with $m$ variables on which the strong version of PPSZ $k$-SAT algorithm, which uses bounded width resolution, has success probability at most $2^{-(1 - (1 + \epsilon)2/k)m}$ for every $\epsilon > 0$. Previously such a bound was known only for the weak PPSZ algorithm which exhaustively searches ... more >>>

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