Potential Game Theoretic Learning for the Minimal Weighted Vertex Cover in Distributed Networking Systems

Abstract

Toward the minimal weighted vertex cover (MWVC) in agent-based networking systems, this paper recasts it as a potential game and proposes a distributed learning algorithm based on relaxed greed and finite memory. With the concept of convention, we prove that our algorithm converges with probability 1 to Nash equilibria, which serve as the bridge connecting the game and the MWVC. More importantly, an additional degree of freedom is also provided for equilibrium refinement, such that increasing memory lengths and mutation probabilities contributes to the improvement of system-level objectives. Comparisons with typical methods, centralized and distributed, demonstrate the advantage of our algorithm for both weighted and unweighted versions. This paper not only provides a useful tool for the MWVC problem in decentralized environments but also paves an effective way for distributed coordination and optimization that could be modeled as potential games.

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

“…Following this line, Balcan et al studied a broad family of covering problems in a distributed setting [21], by carefully constructing an advice vector with the aid of centralized information. Aiming for fully distributed coordination, Sun et al [26] addressed the MWVC problem by decomposing the system-level objective into local utilities and proposed a restricted greed and memory-based algorithm (RGMA) within the framework of potential game theory. To the best knowledge of the authors, the FBR and the RGMA provide the-state-of-the-art results for the distributed MWVC problem.…”

“…We use the prefix "1-" or "0-" to describe a node with a i = 1 or a i = 0, which is also referred to as a selected node or an unselected node. The solution space is given by A = {a|a i ∈ {0, 1}, i ∈ N}, i = {j|(i, j) ∈ E} represents the neighborhood of node i, with i / ∈ i , and coefficient λ is introduced to penalize uncovered edges [26].…”

“…Specifically, the BA network is constructed by following the growth and preferential attachment rule in the BA model [46]: starting from a ring network with n = 5 vertices, at each step, we add a new vertex with two edges linked to the existing vertices. Furthermore, the grid network is used to represent a regular scenario, where each node has the same number of neighbors [26]. As in the literature, the vertex weights are randomly generated, which are then normalized such that i∈N ω i = 1.…”

“…1) RGMA: This algorithm is also designed within the framework of learning in potential games, where each player updates its action according to a restricted greed and unweighted memory rule [26]. Although convergence to Nash equilibria is guaranteed, INEs cannot be avoided.…”

A Reputation-Based Multi-User Task Selection Incentive Mechanism for Crowdsensing

“…Definition 2 (Ordinal Potential Game [31]): If a game is a potential game, then equation : S ⇒ R is a potential function, where S = i S i , for every i ∈ N , s i , s i , ∈ S i , s −i ∈ j =i S j , the following relation exists: 6) Potential game is often applied to spectrum control in wireless network [32], decentralized optimization in channel selection [33], vertex cover problem in wireless sensor networks [34], etc. It owns a Finite Improvement Property (FIP) and always admits NE.…”