Dominating Set Knapsack: Profit Optimization on Dominating Sets
Sipra Singh

TL;DR
This paper introduces the Dominating Set Knapsack problem, combining graph domination with profit maximization under budget constraints, and analyzes its computational complexity and algorithms for special cases.
Contribution
It formally defines the Dominating Set Knapsack problem, proves its complexity results, and develops FPT algorithms for specific graph classes and variants.
Findings
NP-complete on bipartite graphs
Weakly NP-complete on star graphs
Pseudo-polynomial algorithm for trees
Abstract
In a large-scale network, we want to choose some influential nodes to make a profit by paying some cost within a limited budget so that we do not have to spend more budget on some nodes adjacent to the chosen nodes; our problem is the graph-theoretic representation of it. We define our problem, Dominating Set Knapsack, by attaching the knapsack problem with the dominating set on graphs. Each vertex is associated with a cost factor and a profit amount . We aim to choose some vertices within a fixed budget that give maximum profit so that we do not need to choose their 1-hop neighbors. We show that the Dominating Set Knapsack problem is strongly NPC even when restricted to bipartite graphs, but weakly NPC for star graphs. We present a pseudo-polynomial time algorithm for trees in time . We show that Dominating Set…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Vehicle Routing Optimization Methods · Advanced Graph Theory Research
