A Serial Game Distributed Algorithm to ϵ-Minimum Vertex Cover of Networks in Finite Time - Chen, Jie; Zhou, Rongpei; Gui, Weihua (IEEE transactions on automation science and engineering, 2025)
Vertex cover problem is a typical nondeterministic polynomial combinatorial optimization problem with wide applications. In order to seek a near-optimal solution in finite time, this article achieves the goal from the perspective of serial potential game optimization. Specifically, we present the vertex cover problem as a potential game, where the corresponding potential function minimizers are equivalent to the minimum vertex cover state. Then, we propose a novel polynomial-based serial game distributed algorithm, and prove that the algorithm can guarantee that strategies of all vertices converge to a ε -minimum vertex cover ( ε -MVC) state in finite time. Compared with the existing representative optimization algorithms on networks and standard benchmarks, numerical simulations demonstrate our proposed algorithm can effectively balance solution efficiency and computation time. We hope this work provides insight for decision-makers designing a reasonable algorithm when solving nondeterministic polynomial optimization problems, so as to guarantee both solution quality and computation time. Note to Practitioners-Vertex cover problem has a wide range of practical applications. Many distributed optimization algorithms for the vertex cover problem are available in the existing literatures. However, those algorithms mainly pursue high-quality solutions in infinite time. Thus, one of the main challenges is to design a distributed algorithm that guarantees both solution quality and computation time. This article design a polynomial-based serial game algorithm, and prove that it can converge to the ε -MVC state in finite time. This article can serve as a supplement to the existing optimization algorithms for solving the vertex cover problem.