Related papers: Fine-grained Complexity Meets IP = PSPACE
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
We provide a new approach for establishing hardness of approximation results, based on the theory recently introduced by the author. It allows one to directly show that approximating a problem beyond a certain threshold requires…
Sequence alignment is a cornerstone technique in computational biology for assessing similarities and differences among biological sequences. A key variant, sequence-to-graph alignment, plays a crucial role in effectively capturing genetic…
Motivated by penalized likelihood maximization in complex models, we study optimization problems where neither the function to optimize nor its gradient have an explicit expression, but its gradient can be approximated by a Monte Carlo…
Fine-grained complexity theory is the area of theoretical computer science that proves conditional lower bounds based on the Strong Exponential Time Hypothesis and similar conjectures. This area has been thriving in the last decade, leading…
We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…
During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community. The cornerstone of the framework is the notion of…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
It is shown in this note that approximating the number of independent sets in a $k$-uniform linear hypergraph with maximum degree at most $\Delta$ is NP-hard if $\Delta\geq 5\cdot 2^{k-1}+1$. This confirms that for the relevant sampling and…
We present a polylogarithmic local computation matching algorithm which guarantees a $(1-\eps)$-approximation to the maximum matching in graphs of bounded degree.
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…
We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The…
Finding sparse vectors is a fundamental problem that arises in several contexts including codes, subspaces, and lattices. In this work, we prove strong inapproximability results for all these variants using a novel approach that even…
The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
We study a family of problems, called \prob{Maximum Solution}, where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean…
Let $P$ be a polygonal curve in $\mathbb{R}^d$ of length $n$, and $S$ be a point-set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that the Fr\'echet distance from $P$ is less than a…