Edge-Vertex Dominating Set in Unit Disk Graphs

11/26/2021

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by   Vishwanath R. Singireddy, et al.

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Given an undirected graph G=(V,E), a vertex v∈ V is edge-vertex (ev) dominated by an edge e∈ E if v is either incident to e or incident to an adjacent edge of e. A set S^ev⊆ E is an edge-vertex dominating set (referred to as ev-dominating set) of G if every vertex of G is ev-dominated by at least one edge of S^ev. The minimum cardinality of an ev-dominating set is the ev-domination number. The edge-vertex dominating set problem is to find a minimum ev-domination number. In this paper we prove that the ev-dominating set problem is NP-hard on unit disk graphs. We also prove that this problem admits a polynomial-time approximation scheme on unit disk graphs. Finally, we give a simple 5-factor linear-time approximation algorithm.