A BRANCH AND BOUND ALGORITHM FOR FINDING THE POSITIVE INFLUENCE DOMINATING SET ON CHORDAL GRAPHS
TL;DR
This paper develops an exact algorithm based on the Branch and Bound approach for solving PIDS on chordal graphs, which involves identifying the smallest group of vertices in a given network that maximizes influence throughout the network.
Abstract
ABSTRACT We address the Positive Influence Dominating Set problem (PIDS), which involves identifying the smallest group of vertices in a given network that maximizes influence throughout the network. Formally, given a graph G = (V, E), representing the network, we look for a subset of vertices P ⊆ V such that each vertex v i ∈ V \ P has at least ρ deg G (v i ) neighbors in P, where deg G (v i ) is the degree of v i , and 0 < ρ < 1. The problem is known to be NP-hard in general graphs and remains NP-hard even when restricted to certain particular classes, such as chordal graphs. In this paper, we develop an exact algorithm based on the Branch and Bound approach for solving PIDS on chordal graphs. The effectiveness of the proposed algorithm is demonstrated through numerical experiments conducted on various randomly generated chordal graphs.