Algorithms for core stability, core largeness, exactness, and extendability of flow games

Authors:
Qizhi Fang;Rudolf Fleischer;Jian Li;Xiaoxun Sun
Affiliations:
Department of Mathematics, Ocean University of China, Qingdao, China;Department of Computer Science and Engineering Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Computer Science and Engineering Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Mathematics and Computing, University of Southern Queensland
Venue:
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Year:
2007

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Abstract

In this paper, we give linear time algorithms to decide core stability, core largeness, exactness, and extendability of flow games on uniform networks (all edge capacities are 1). We show that a uniform flow game has a stable core if and only if the network is a balanced DAG (for all non-terminal vertices, indegree equals outdegree), which can be decided in linear time. Then we show that uniform flow games are exact, extendable, and have a large core if and only if the network is a balanced directed series-parallel graph, which again can be decided in linear time.