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Efficient Algorithms for Games Played on Trees with Back-edges

Gandhi A., Khoussainov B., Liu J.

Fundamenta Informaticae

2011

Vol. 111, nr 4

391-412

This paper studies algorithms for deciding the winners of two-player games played on directed graphs. We focus on the case when the underlying graphs are trees with back-edges and provide both theoretical and experimental analysis of this class of games. In particular, we present an algorithm that solves Büchi games played on trees with back-edges in time O(min{r źm, l+m}) where m is the number of edges, l is the sum of the distances from the root to all leaves and the parameter r is bounded by the height of the tree. We also show that parity games played on trees with back-edges can be solved in time O(l + m).