Output-sensitive algorithm for the edge-width of an embedded graph

Let G be an unweighted graph of complexity n cellularly embedded in a surface (orientable or not) of genus g. We describe improved algorithms to compute (the length of) a shortest non-contractible and a shortest non-separating cycle of G. If k is an integer, we can compute such a non-trivial cycle with length at most k in O(gnk) time, or correctly report that no such cycle exists. In particular, on a fixed surface, we can test in linear time whether the edge-width or face-width of a graph is bounded from above by a constant. This also implies an output-sensitive algorithm to compute a shortest non-trivial cycle that runs in O(gnk) time, where k is the length of the cycle. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical algorithms and problems—Computations on discrete structures; Geometric problems and computations; G.2.2 [Discrete Mathematics]: Graph theory—Graph algorithms; path and circuit problems; I.3.5 [Computer Graphic...

• Type: Conference
• Year: 2010
• Where: COMPGEOM
• Authors: Sergio Cabello, Éric Colin de Verdière, Francis Lazarus
• Keywords: Algorithms, COMPGEOM 2010, Non-trivial Cycle, Shortest Non-separating Cycle