Better Approximation for Distributed Weighted Vertex Cover via Game-Theoretic Learning

Abstract

Toward better approximation for the minimumweighted vertex cover (MWVC) problem in multiagent systems, we present a distributed algorithm from the perspective of learning in games. For self-organized coordination and optimization, we see each vertex as a potential game player who makes decisions using local information of its own and the immediate neighbors. The resulting Nash equilibrium is classified into two categories, i.e., the inferior Nash equilibrium (INE) and the dominant Nash equilibrium (DNE). We show that the optimal solution must be a DNE. To achieve better approximation ratios, local rules of perturbation and weighted memory are designed, with the former destroying the stability of an INE and the latter facilitating the refinement of a DNE. By showing the existence of an improvement path from any INE to a DNE, we prove that when the memory length is larger than 1, our algorithm converges in finite time to DNEs, which could not be improved by exchanging the action of a selected node with all its unselected neighbors. Moreover, additional freedom for solution efficiency refinement is provided by increasing the memory length. Finally, intensive comparison experiments demonstrate the superiority of the presented methodology to the state of the art, both in solution efficiency and computation speed.

Two‐stage and three‐stage recursive gradient identification of Hammerstein nonlinear systems based on the key term separation

“…The proposed algorithm in this article can be allied to model some industrial process systems. [117][118][119][120][121][122][123][124][125][126][127]…”

“…The effectiveness of the presented methods have been verified by the simulation, and the accuracy of parameter estimation can be improved by using hierarchical identification principle. The proposed algorithm in this article can be allied to model some industrial process systems 117‐127 …”

An Interactive Application for Learning and Analyzing Different Graph Vertex Cover Algorithms

“…Thus, the optimal cover contains at least one of the two vertices of any edge, i.e., any one covering set of a given graph will be at most twice as large (in power) as the optimal covering set for that graph [30]. There are also algorithmic techniques where the coefficient of approximation to the optimal solution is smaller [31,32].…”