Dynamic Dominating Probability-Driven Fuzzy Iterative Algorithm for Identifying Positive Influence Dominating Sets

Abstract

The Minimum Positive Influence Dominating Set problem, an NP-hard extension of the classical dominating set, plays a crucial role in social network analysis by identifying a minimal node set that ensures majority positive influence coverage. Conventional approaches, including exact solvers, greedy heuristics, and metaheuristics, are hindered by prohibitive computational costs, proneness to local optima, or excessive parameter sensitivity. This study introduces a Dynamic Dominating ProbabilityDriven Fuzzy Iterative Algorithm to tackle these limitations. The proposed method employs a dynamic local probability metric to assess each candidate node’s contribution toward satisfying residual domination demands of its neighbors, with individual thresholds defined as half the node degree. By iteratively selecting the highest-probability node, incorporating implicit fuzzy-inspired probabilistic handling of uncertainty, and performing real-time status updates, the algorithm effectively mitigates local optima traps while achieving O(n3) time complexity. Experimental evaluations on benchmark networks demonstrate superior solution quality and faster convergence compared to standard baselines.OPEN ACCESS Received: 03/01/2026 Accepted: 12/03/2026 Published: 21/07/2026

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