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COMPGEOM
2010
ACM

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

13 years 8 months ago
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...
Sergio Cabello, Éric Colin de Verdiè
Added 10 Jul 2010
Updated 10 Jul 2010
Type Conference
Year 2010
Where COMPGEOM
Authors Sergio Cabello, Éric Colin de Verdière, Francis Lazarus
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