Related papers: Iterative Partial Rounding for Vertex Cover with H…
$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
This paper gives poly-logarithmic-round, distributed D-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio D is the maximum number of…
Conformal Prediction (CP) is a popular uncertainty quantification method that provides distribution-free, statistically valid prediction sets, assuming that training and test data are exchangeable. In such a case, CP's prediction sets are…
Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
In the NP-hard \textsc{Group Closeness Centrality Maximization} problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that maximizes the reciprocal of group farness…
In this paper we construct an approximation algorithm for the Minimum Vertex Cover Problem (Min-VC) with an expected approximation ratio of 2-f(beta) for random Power Law Graphs (PLG) in the (alpha,beta)-model of Aiello et. al., where…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We present the first formal verification of approximation algorithms for NP-complete optimization problems: vertex cover, independent set, set cover, center selection, load balancing, and bin packing. We uncover incompletenesses in existing…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
We show a new way to round vector solutions of semidefinite programming (SDP) hierarchies into integral solutions, based on a connection between these hierarchies and the spectrum of the input graph. We demonstrate the utility of our method…
In the classic Correlation Clustering problem introduced by Bansal, Blum, and Chawla (FOCS 2002), the input is a complete graph where edges are labeled either $+$ or $-$, and the goal is to find a partition of the vertices that minimizes…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…
We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\eps)$-approximation to the…
We provide CONGEST model algorithms for approximating minimum weighted vertex cover and the maximum weighted matching. For bipartite graphs, we show that a $(1+\varepsilon)$-approximate weighted vertex cover can be computed…
The aim of this paper is to present a method for computation of persistent homology that performs well at large filtration values. To this end we introduce the concept of filtered covers. We show that the persistent homology of a bounded…
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance.…