Coalition structure generation with worst case guarantees

Tuomas Sandholm, Kate Larson, Martin Andersson, Onn Shehory, Fernando Tohmé

Research output: Contribution to journalArticlepeer-review

600 Scopus citations


Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NP-complete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents.

Original languageEnglish
Pages (from-to)209-238
Number of pages30
JournalArtificial Intelligence
Issue number1
StatePublished - Jul 1999
Externally publishedYes

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation under CAREER Award IRI-9703122, Grant IRI-9610122, and Grant IIS-9800994.


Dive into the research topics of 'Coalition structure generation with worst case guarantees'. Together they form a unique fingerprint.

Cite this