Capacitated Partition Vertex Cover and Partition Edge Cover
Rajni Dabas, Samir Khuller, Emilie Rivkin

TL;DR
This paper introduces approximation algorithms for the Capacitated Partition Vertex Cover problem in hypergraphs, addressing both soft and hard capacity variants, and also presents an exact polynomial-time algorithm for a related edge cover problem.
Contribution
It provides the first approximation algorithms for capacitated partition vertex cover in hypergraphs and an exact polynomial-time solution for the weighted partition edge cover problem.
Findings
$(f+1)$-approximation for weighted soft-capacitated C-PVC
$(f+ ext{epsilon})$-approximation for unweighted hard-capacitated C-PVC
First exact polynomial-time algorithm for weighted partition edge cover
Abstract
Our first focus is the Capacitated Partition Vertex Cover (C-PVC) problem in hypergraphs. In C-PVC, we are given a hypergraph with capacities on its vertices and a partition of the hyperedge set into distinct groups. The objective is to select a minimum size subset of vertices that satisfies two main conditions: (1) in each group, the total number of covered hyperedges meets a specified threshold, and (2) the number of hyperedges assigned to any vertex respects its capacity constraint. A covered hyperedge is required to be assigned to a selected vertex that belongs to the hyperedge. This formulation generalizes classical Vertex Cover, Partial Vertex Cover, and Partition Vertex Cover. We investigate two primary variants: soft capacitated (multiple copies of a vertex are allowed) and hard capacitated (each vertex can be chosen at most once). Let denote the rank of the…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Computational Geometry and Mesh Generation · Advanced Graph Theory Research
