Faster Shortest Non-contractible Cycles in Directed Surface Graphs

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((g3 + 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((g2 + g b)n log n) time, generalizing a known algorithm to compute the shortest non-separating cycle. ∗Department of Computer Science, University of Illinois, Urbana-Champaign; [email protected]. Research supported in part by the Department of Energy Office of Science Graduate Fellowship Program (DOE SCGF), made possible in part by the American Recovery and Reinvestment Act of 2009, administered by ORISE-ORAU under contract no. DE-AC05-06OR23100.