Solving Coalition Structure Generation Problems over Weighted Graph

Emi Watanabe, Miyuki Koshimura, Yuko Sakurai, Makoto Yokoo

Abstract: Coalition Structure Generation (CSG), which is a leading research issue in the domain of coalitional games, divides agents into exhaustive and disjoint coalitions to optimize social welfare. This paper studies CSG problems over weighted undirected graphs in which the weight on an edge between any two connecting agents represents how well they work together in a coalition. The weight can have either a positive or a negative value. We examine two types of problems. One is a CSG without any restrictions on the number of coalitions, and another is a CSG with k coalitions where k is determined in advance. We present two methods to solve these problems: ILP formulation and MaxSAT encoding.