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Electronic Colloquium on Computational Complexity

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Reports tagged with fine-grained complexity:
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 >>>

TR17-130 | 30th August 2017
Oded Goldreich, Guy Rothblum

Worst-case to Average-case reductions for subclasses of P

Revisions: 4

For every polynomial $q$, we present worst-case to average-case (almost-linear-time) reductions for a class of problems in $\cal P$ that are widely conjectured not to be solvable in time $q$.
These classes contain, for example, the problems of counting the number of $k$-cliques in a graph, for any fixed $k\geq3$.
more >>>

TR18-092 | 4th May 2018
Marco Carmosino, Russell Impagliazzo, Manuel Sabin

Fine-Grained Derandomization: From Problem-Centric to Resource-Centric Complexity

We show that popular hardness conjectures about problems from the field of fine-grained complexity theory imply structural results for resource-based complexity classes. Namely, we show that if either k-Orthogonal Vectors or k-CLIQUE requires $n^{\epsilon k}$ time, for some constant $\epsilon > 1/2$, to count (note that these conjectures are significantly ... more >>>

TR18-210 | 30th November 2018
Karthik C. S., Pasin Manurangsi

On Closest Pair in Euclidean Metric: Monochromatic is as Hard as Bichromatic

Given a set of $n$ points in $\mathbb R^d$, the (monochromatic) Closest Pair problem asks to find a pair of distinct points in the set that are closest in the $\ell_p$-metric. Closest Pair is a fundamental problem in Computational Geometry and understanding its fine-grained complexity in the Euclidean metric when ... 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 >>>

TR19-125 | 27th August 2019
Elazar Goldenberg, Karthik C. S.

Hardness Amplification of Optimization Problems

In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products.

We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently aggregate any $k$ instances of $\Pi$ and form one large instance ... more >>>

TR19-135 | 2nd October 2019
Michel Goemans, Shafi Goldwasser, Dhiraj Holden

Doubly-Efficient Pseudo-Deterministic Proofs

In [20] Goldwasser, Grossman and Holden introduced pseudo-deterministic interactive proofs for search problems where a powerful prover can convince a probabilistic polynomial time verifier that a solution to a search problem is canonical. They studied search problems for which polynomial time algorithms are not known and for which many solutions ... more >>>

TR20-177 | 12th October 2020
Lior Gishboliner, Yevgeny Levanzov, Asaf Shapira

Counting Subgraphs in Degenerate Graphs

We consider the problem of counting the number of copies of a fixed graph $H$ within an input graph $G$. This is one of the most well-studied algorithmic graph problems, with many theoretical and practical applications. We focus on solving this problem when the input $G$ has {\em bounded degeneracy}. ... more >>>

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