Related papers: An exact algorithm with the time complexity of $O^…
We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…
In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\epsilon(m)$-time algorithms for $(1-\epsilon)$-maximum weight $f$-factor and…
Many combinatorial problems involving weights can be formulated as a so-called ranged problem. That is, their input consists of a universe $U$, a (succinctly-represented) set family $\mathcal{F} \subseteq 2^{U}$, a weight function $\omega:U…
We consider a variant of the set covering problem with uncertain parameters, which we refer to as the chance-constrained set multicover problem (CC-SMCP). In this problem, we assume that there is uncertainty regarding whether a selected set…
Given a weighted bipartite graph $G = (L, R, E, w)$, the maximum weight matching (MWM) problem seeks to find a matching $M \subseteq E$ that maximizes the total weight $\sum_{e \in M} w(e)$. This paper presents a novel algorithm with a time…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every…
Recently, the first online complexity class, AOC, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted…
Let c denote a non-negative constant. Suppose that we are given an edge-weighted bipartite graph G=(V,E) with its 2-layered drawing and a family X of intersecting edge pairs. We consider the problem of finding a maximum weighted matching M*…
In this article we propose a Weighted Stochastic Mesh (WSM) Algorithm for approximating the value of a discrete and continuous time optimal stopping problem. We prove that in the discrete case the WSM algorithm leads to semi-tractability of…
The Optimal Morse Matching (OMM) problem asks for a discrete gradient vector field on a simplicial complex that minimizes the number of critical simplices. It is NP-hard and has been studied extensively in heuristic, approximation, and…
In the $k$-cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. The current best algorithms are an…
We study the maximum set coverage problem in the massively parallel model. In this setting, $m$ sets that are subsets of a universe of $n$ elements are distributed among $m$ machines. In each round, these machines can communicate with each…
In this work, we study the trade-off between the running time of approximation algorithms and their approximation guarantees. By leveraging a structure of the `hard' instances of the Arora-Rao-Vazirani lemma [JACM'09], we show that the…
The $k$-ExactCover problem is a parameterized version of the ExactCover problem, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and an integer $k$, and the task is to determine whether $U$ can be partitioned into…
Fishburn developed an algorithm to solve a system of $m$ difference constraints whose $n$ unknowns must take values from a set with $k$ real numbers [Solving a system of difference constraints with variables restricted to a finite set,…
We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and…
We study the Euclidean minimum weight perfect matching problem for $n$ points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on $n$ requires at least $\Omega(n \log n)$ time.…