Partitioned Combinatorial Optimization Games

TL;DR

This paper introduces a new class of cooperative games called Partitioned Combinatorial Optimization Games, analyzing their core stability and computational complexity for key graph optimization problems.

Contribution

It defines PCOGs, explores core stability verification and existence, and analyzes their complexity for four fundamental graph optimization tasks.

Findings

Core stability verification is computationally hard for several problems.

Core existence can be undecidable in general.

Complexity varies across different combinatorial optimization problems.

Abstract

We propose a class of cooperative games, called d Partitioned Compbinatorial Optimization Games (PCOGs). The input of PCOG consists of a set of agents and a combinatorial structure (typically a graph) with a fixed optimization goal on this structure (e.g., finding a minimum dominating set on a graph) such that the structure is divided among the agents. The value of each coalition of agents is derived from the optimal solution for the part of the structure possessed by the coalition. We study two fundamental questions related to the core: Core Stability Verification and Core Stability Existence. We analyze the algorithmic complexity of both questions for four classic graph optimization tasks: minimum vertex cover, minimum dominating set, minimum spanning tree, and maximum matching.