An Optimal Integer Partition Approach to Coalition Structure Generation

Abstract

This paper proposes a new solution to the problem of coalition structure generation using an optimal integer partition. The new partition is the set of set of integers where each integer represents size of a coalition. It includes only elements that no other elements in this partition have values of generated structures higher than them. We show that an element of this partition is a set containing 1 at most one element. Any solutions to the problem of coalition structure generation using the new partition can reduce at least approximately 40% of possible candidate structures when size of coalition members at least 5. Moreover, the bigger the size of coalition members is, the more these solutions outperform the ones using integer partitions.