Extended formulations for perfect domination problems and their algorithmic implications

Vinicius L. do Forte, Saïd Hanafi and Abilio Lucena

European Journal of Operational Research, 2023, vol. 310, issue 2, 566-581

Abstract: Given an undirected graph G=(V,E), a subset D⊆V is called a vertex dominating set (VDS) if every vertex of V either belongs to D or is adjacent to a vertex of D. Additionally, a VDS D is called perfect if every vertex of V∖D is adjacent to a single vertex of D. Finally, the Perfect Vertex Domination Problem (PVDP) asks for a perfect VDS D with the smallest cardinality possible. Domination extends very naturally to the edges of G=(V,E) and the Perfect Edge Domination Problem (PEDP) asks for a perfect edge dominating set with as few edges as possible. We propose new formulations for PVDP and PEDP. They rely on structural properties of perfect dominating sets and are computationally compared with their counterparts from the literature. For the new PEDP formulation, in particular, running times for standard state-of-the-art mixed integer programming codes are shown to frequently lead to speed-ups of orders of magnitude, over their corresponding performances for the remaining PEDP formulations.

Keywords: Combinatorial optimization; Perfect graph domination; Mathematical formulations; Exact solution algorithms; Computational results (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:310:y:2023:i:2:p:566-581

DOI: 10.1016/j.ejor.2023.03.022

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