Computer Science – Computer Science and Game Theory
Scientific paper
2010-11-30
Computer Science
Computer Science and Game Theory
15 pages, algorithm pessimistic complexity O(n 2^(n/2)), pseudopolynomial complexity O(nq), calculates Banzhaf indices of all
Scientific paper
In this paper new algorithm for calculating power indices is described. The complexity class of the problem is #P-complete and even calculating power index of the biggest player is NP-hard task. Constructed algorithm is a mix of ideas of two algorithms: Klinz & Woeginger partitioning algorithm and Mann & Shapley generating functions algorithm. Time and space complexities of the algorithm are analysed and compared with other known algorithms for the problem. Constructed algorithm has pessimistic time complexity O(n 2^(n/2))and pseudopolynomial complexity O(nq), where q is quota of the voting game. This paper also solves open problem stated by H. Aziz and M. Paterson - existence of the algorithm for calculating Banzhaf power indices of all players with time complexity lower than O(n^2 2^(n/2)). Not only is the answer positive but this can be done keeping the pseudopolynomial complexity of generating functions algorithm in case weights are integers. New open problems are stated.
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