{"paper":{"title":"Graph Coalition Structure Generation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CC","cs.GT","cs.MA"],"primary_cat":"cs.DS","authors_text":"Maria Polukarov, Nicholas R. Jennings, Thomas D. Voice","submitted_at":"2011-02-08T23:13:58Z","abstract_excerpt":"We give the first analysis of the computational complexity of {\\it coalition structure generation over graphs}. Given an undirected graph $G=(N,E)$ and a valuation function $v:2^N\\rightarrow\\RR$ over the subsets of nodes, the problem is to find a partition of $N$ into connected subsets, that maximises the sum of the components' values. This problem is generally NP--complete; in particular, it is hard for a defined class of valuation functions which are {\\it independent of disconnected members}---that is, two nodes have no effect on each other's marginal contribution to their vertex separator. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1747","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}