Work

On the complexity of the vector connectivity problem

Year: 2014

Type: article

Abstract: We study a relaxation of the Vector Domination problem called Vector Connectivity (VecCon). Given a graph $G$ with a requirement $r(v)$ for each vertex $v$, VecCon asks for a minimum cardinality set $S$ of vertices such that every vertex $v\in V\setminus S$ is connected to $S$ via $r(v)$ disjoint paths. In the paper introducing the problem, Boros et al. [Networks, 2014] gave polynomial-time solutions for VecCon in trees, cographs, and split graphs, and showed that the problem can be approximated in polynomial time on $n$-vertex graphs to within a factor of $\log n+2$, leaving open the question of whether the problem is NP-hard on general graphs. We show that VecCon is APX-hard in general graphs, and NP-hard in planar bipartite graphs and in planar line graphs. We also generalize the polynomial result for trees by solving the problem for block graphs.

Source: Repository of the University of Primorsk (University of Primorska)

DOI: 10.48550/arxiv.1412.2559

Authors: Cicalese, Ferdinando, Milanič, Martin, Rizzi, Romeo

Institutions: University of Verona, University of Salerno, University of Primorska

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Science Foundation, Javna Agencija za Raziskovalno Dejavnost RS