Fang, Qizhi and Fleischer, Rudolf and Li, Jian and Sun, Xiaoxun (2007) Algorithms for core stability, core largeness, exactness, and extendability of flow games. In: COCOON 2007: 13th Annual International Computing and Combinatorics Conference, 16-19 Jul 2007, Banff, Canada.
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.
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