Shortest non-trivial cycles in directed surface graphs

Jeff Erickson
2011 Proceedings of the 27th annual ACM symposium on Computational geometry - SoCG '11  
Let G be a directed graph embedded on a surface of genus g. We describe an algorithm to compute the shortest non-separating cycle in G in O(g 2 n log n) time, exactly matching the fastest algorithm known for undirected graphs. We also describe an algorithm to compute the shortest non-contractible cycle in G in g O(g) n log n time, matching the fastest algorithm for undirected graphs of constant genus.
doi:10.1145/1998196.1998231 dblp:conf/compgeom/Erickson11 fatcat:zndqeloqv5b3fa5h6da6ns2om4