On the [formula omitted]-Strong Roman Domination Problem

Abstract

The Roman domination problem (RDP) aims to find an optimal strategy to defend a graph or network with the least number of defenders. Although it holds great application potential to many fields, the RDP is mostly studied from theoretical aspects. In this paper, we extend the RDP and bridge the gap between theory and practice. Specifically, we define the k-strong Roman domination problem (k-SRDP), where defenders are assigned to a network to repel multiple simultaneous attacks. We propose an integer programming formulation of the problem, as well as a two-stage stochastic formulation using Benders decomposition. We show that the problem scale grows rapidly as the instance becomes larger. We prove the integrality of the second stage and propose two algorithms based on the L-shaped method. The algorithms are compared using randomly generated graph instances. Experimental results suggest that the proposed algorithms can solve the k-SRDP efficiently.