Constant factor approximation algorithms for coalition structure generation

Abstract

Coalition structure generation is a central problem in characteristic function games. Most algorithmic work to date can be classified into one of three broad categories: anytime algorithms, design-to-time algorithms and heuristic algorithms [5]. This paper focuses on the former two approaches. Both design-to-time and anytime algorithms have pros and cons. While design-to-time algorithms guarantee finding an optimal solution, they must be run to completion in order to generate any solution. Anytime algorithms; however, permit premature termination while providing solutions of ever increasing quality along with quality guarantees. Design-to-time algorithms have a better worst case runtime (O(3 n ) for n agents) compared to the current anytime algorithms (O(n n ) for n agents), but do not provide the flexibility of anytime algorithms. In this paper we present the first design-to-time constant factor approximation algorithms for coalition structure generation that guarantee high quality solutions quickly. We show how our approach can be used as an anytime algorithm, which combines both the worst case runtime of the design-to-time algorithms and the flexibility of the anytime algorithms. This results in the first anytime algorithm for coalition structure generation which has the same worst case time complexity of the current best design-to-time algorithms.