Integer linear programming models for the weighted total domination problem

Yuede Ma, Qingqiong Cai and Shunyu Yao

Applied Mathematics and Computation, 2019, vol. 358, issue C, 146-150

Abstract: A total dominating set of a graph G=(V,E) is a subset D of V such that every vertex in V (including the vertices from D) has at least one neighbour in D. Suppose that every vertex v ∈ V has an integer weight w(v) ≥ 0 and every edge e ∈ E has an integer weight w(e) ≥ 0. Then the weighted total domination (WTD) problem is to find a total dominating set D which minimizes the cost f(D):=∑u∈Dw(u)+∑e∈E[D]w(e)+∑v∈V∖Dmin{w(uv)|u∈N(v)∩D}. In this paper, we put forward three integer linear programming (ILP) models with a polynomial number of constraints, and present some numerical results implemented on random graphs for WTD problem.

Keywords: Weighted total domination; Integer linear programming; Combinatorial optimization; Graph theory (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:358:y:2019:i:c:p:146-150

DOI: 10.1016/j.amc.2019.04.038

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