相关论文: Optimal PSPACE-hardness of Approximating Set Cover…

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…

Sublinear time algorithms for approximating maximum matching size have long been studied. Much of the progress over the last two decades on this problem has been on the algorithmic side. For instance, an algorithm of Behnezhad [FOCS'21]…

We investigate the polynomial-time approximability of the multistage version of Min-Sum Set Cover ($\mathrm{DSSC}$), a natural and intriguing generalization of the classical List Update problem. In $\mathrm{DSSC}$, we maintain a sequence of…

We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…

We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [RSW18]. Graph algorithms in this cut query model and other query models have recently been studied for various…

We study minimum vertex cover problems on random \alpha-uniform hypergraphs using two different approaches, a replica method in statistical mechanics of random systems and a leaf removal algorithm. It is found that there exists a phase…

We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set. Given a red-blue bipartite graph $G$ and an auxiliary connectivity graph $G_{conn}$ on red vertices, and integers $k, t$, the…

Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…

A classic result of Williamson, Goemans, Mihail, and Vazirani [STOC 1993: 708-717] states that the problem of covering an uncrossable set family by a min-cost edge set admits approximation ratio $2$, by a primal-dual algorithm with a…

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on…

In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…

The densest k-subgraph (DkS) problem (i.e. find a size k subgraph with maximum number of edges), is one of the notorious problems in approximation algorithms. There is a significant gap between known upper and lower bounds for DkS: the…

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games…

The \emph{Dominating $H$-Pattern} problem generalizes the classical $k$-Dominating Set problem: for a fixed \emph{pattern} $H$ and a given graph $G$, the goal is to find an induced subgraph $S$ of $G$ such that (1) $S$ is isomorphic to $H$,…

This paper studies the computational complexity of the Edge Packing problem and the Vertex Packing problem. The edge packing problem (denoted by $\bar{EDS}$) and the vertex packing problem (denoted by $\bar{DS} $) are linear programming…

In the $(k,h)$-SetCover problem, we are given a collection $\mathcal{S}$ of sets over a universe $U$, and the goal is to distinguish between the case that $\mathcal{S}$ contains $k$ sets which cover $U$, from the case that at least $h$ sets…

The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…

Given a weighted hypergraph $\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$, the approximate $k$-cover problem seeks for a size-$k$ subset of $V$ that has the maximum weighted coverage by \emph{sampling only a few hyperedges} in…

Consider an agent traversing a graph of "gadgets", each with local state that changes with each traversal by the agent. We characterize the complexity of universal traversal, where the goal is to traverse every gadget at least once, for DAG…

In this paper we focus on problems which do not admit a constant-factor approximation in polynomial time and explore how quickly their approximability improves as the allowed running time is gradually increased from polynomial to…