Faster Shortest Non-contractible Cycles in Directed Surface Graphs

Details Faster Shortest Non-contractible Cycles in Directed Surface Graphs Faster Shortest Non-contractible Cycles in Directed Surface Graphs

2011-11-29

arxiv.org/abs/1111.6990v2

Computer Science

Computational Geometry

Scientific paper

Let G be a directed graph embedded on a surface of genus g with b boundary cycles. We describe an algorithm to compute the shortest non-contractible cycle in G in O((g^3 + g b) n log n) time. Our algorithm improves the previous best known time bound of (g + b)^O(g+b) n log n for all positive g and b. We also describe an algorithm to compute the shortest non-null-homologous cycle in G in O((g^2 + g b) n log n) time, generalizing a known algorithm to compute the shortest non-separating cycle.

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