Related papers: Constant Approximating Parameterized $k$-SetCover …

In this paper, we show how one may (efficiently) construct two types of extremal combinatorial objects whose existence was previously conjectural. (*) Panchromatic Graphs: For fixed integer k, a k-panchromatic graph is, roughly speaking, a…

We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…

The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…

We prove that weighted circuit satisfiability for monotone or antimonotone circuits has no fixed-parameter tractable approximation algorithm with any approximation ratio function $\rho$, unless $FPT\neq W[1]$. In particular, not having such…

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…

We consider the question of approximating Max 2-CSP where each variable appears in at most $d$ constraints (but with possibly arbitrarily large alphabet). There is a simple $(\frac{d+1}{2})$-approximation algorithm for the problem. We prove…

In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been…

In $(k,r)$-Center we are given a (possibly edge-weighted) graph and are asked to select at most $k$ vertices (centers), so that all other vertices are at distance at most $r$ from a center. In this paper we provide a number of tight…

A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a…

The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized…

Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…

We study the Equitable Connected Partition (ECP for short) problem, where we are given a graph G=(V,E) together with an integer p, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G…

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique…

In the weighted partial vertex cover problem (WPVC), we are given a graph $G=(V,E)$, cost function $c:V\rightarrow N$, profit function $p:E\rightarrow N$, and positive integers $R$ and $L$. The goal is to check whether there is a subset…

Let $G=(V, E)$ be a given edge-weighted graph and let its {\em realization} $\mathcal{G}$ be a random subgraph of $G$ that includes each edge $e \in E$ independently with probability $p$. In the {\em stochastic matching} problem, the goal…

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…

We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show…

We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false, for…

We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…