Sciweavers

Share
COMPGEOM
2009
ACM

Minimum cuts and shortest homologous cycles

10 years 9 months ago
Minimum cuts and shortest homologous cycles
We describe the first algorithms to compute minimum cuts in surface-embedded graphs in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, our algorithm computes a minimum (s, t)-cut in gO(g) nlog n time. Except for the special case of planar graphs, for which O(nlog n)-time algorithms have been known for more than 20 years, the best previous time bounds for finding minimum cuts in embedded graphs follow from algorithms for general sparse graphs. A slight generalization of our minimum-cut algorithm computes a minimum-cost subgraph in every 2-homology class. We also prove that finding a minimum-cost subgraph homologous to a single input cycle is NP-hard. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—Computations on discrete structures; G.2.2 [Discrete Mathematics]: Graph theory—Graph algorithms General Terms: Algorithms, Pe...
Erin W. Chambers, Jeff Erickson, Amir Nayyeri
Added 28 May 2010
Updated 28 May 2010
Type Conference
Year 2009
Where COMPGEOM
Authors Erin W. Chambers, Jeff Erickson, Amir Nayyeri
Comments (0)
books