Minimum Search to Establish Worst-Case Guarantees in Coalition Structure Generation

Coalition formation is a fundamental research topic in multi-agent systems. In this context, while it is desirable to generate a coalition structure that maximizes the sum of the values of the coalitions, the space of possible solutions is often too large to allow exhaustive search. Thus, a fundamental open question in this area is the following: Can we search through only a subset of coalition structures, and be guaranteed to find a solution that is within a desirable bound � from optimum? If so, what is the minimum such subset? To date, the above question has only been partially answered by Sandholm et al. in their seminal work on anytime coalition structure generation [Sandholm et al., 1999]. More specifically, they identified minimum subsets to be searched for two particular bounds: � = n and � = dn=2e. Nevertheless, the question remained open for other values of �. In this paper

[1]  Nicholas R. Jennings,et al.  Generating coalition structures with finite bound from the optimal guarantees , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[2]  Sandip Sen,et al.  Searching for optimal coalition structures , 2000, Proceedings Fourth International Conference on MultiAgent Systems.

[3]  Sarit Kraus,et al.  Methods for Task Allocation via Agent Coalition Formation , 1998, Artif. Intell..

[4]  Nicholas R. Jennings,et al.  Coalition Structure Generation in Multi-Agent Systems with Positive and Negative Externalities , 2009, IJCAI.

[5]  Victor R. Lesser,et al.  Coalitions Among Computationally Bounded Agents , 1997, Artif. Intell..

[6]  Vincent Conitzer,et al.  Coalition Structure Generation Utilizing Compact Characteristic Function Representations , 2011 .

[7]  Katia P. Sycara,et al.  Customer coalitions in the electronic marketplace , 2000, AGENTS '00.

[8]  Nicholas R. Jennings,et al.  Overlapping Coalition Formation , 2008, WINE.

[9]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[10]  Onn Shehory,et al.  Coalition structure generation with worst case guarantees , 2022 .

[11]  Sarvapali D. Ramchurn,et al.  An Anytime Algorithm for Optimal Coalition Structure Generation , 2014, J. Artif. Intell. Res..

[12]  Nicholas R. Jennings,et al.  Anytime coalition structure generation in multi-agent systems with positive or negative externalities , 2012, Artif. Intell..