1 research outputs found
Minimum Cuts in Surface Graphs
We describe algorithms to efficiently compute minimum -cuts and global
minimum cuts of undirected surface-embedded graphs. Given an edge-weighted
undirected graph with vertices embedded on an orientable surface of
genus , our algorithms can solve either problem in
or time, whichever is better. When is a constant, our
time algorithms match the best running times known for
computing minimum cuts in planar graphs.
Our algorithms for minimum cuts rely on reductions to the problem of finding
a minimum-weight subgraph in a given -homology class, and we give
efficient algorithms for this latter problem as well. If is embedded on a
surface with boundary components, these algorithms run in and time. We also prove that finding
a minimum-weight subgraph homologous to a single input cycle is NP-hard,
showing it is likely impossible to improve upon the exponential dependencies on
for this latter problem.Comment: Unifies and improves upon contributions by different subsets of the
authors that appeared in SoCG 2009, SODA 2011, and SODA 201