Coalition structure generation over graphs

Voice, Thomas, Polukarov, Maria and Jennings, Nicholas R. (2012) Coalition structure generation over graphs. Journal of Artificial Intelligence Research, 45, 165-196. (doi:10.1613/jair.3715).


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We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R 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 independent of disconnected members that is, two nodes have no effect on each others marginal con- tribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP complete for planar graphs, and hence, for any K_k minor free graphs where k ≥ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m^2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph.

Item Type: Article
ISSNs: 1076-9757
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Agents, Interactions & Complexity
ePrint ID: 342780
Date Deposited: 13 Sep 2012 11:31
Last Modified: 14 Apr 2014 11:45
Funded by: EPSRC (EP/I011587/1)
Led by: Nick Jennings
1 January 2011 to 31 December 2015
Further Information:Google Scholar
ISI Citation Count:0

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