699 research outputs found

    Edge-Vertex Dominating Set in Unit Disk Graphs

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    Given an undirected graph G=(V,E)G=(V,E), a vertex v∈Vv\in V is edge-vertex (ev) dominated by an edge e∈Ee\in E if vv is either incident to ee or incident to an adjacent edge of ee. A set SevβŠ†ES^{ev}\subseteq E is an edge-vertex dominating set (referred to as ev-dominating set) of GG if every vertex of GG is ev-dominated by at least one edge of SevS^{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 {\tt 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
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