Year: 2013
Type: article
Abstract: We describe several results on combinatorial optimization problems for graphs where the input comes with an embedding on an orientable surface of small genus. While the specific techniques used differ between problems, all the algorithms we describe share one common feature in that they rely on the al-gebraic topology construct of homology. We describe algorithms to compute global minimum cuts and count minimum s, t-cuts. We describe new algo-rithms to compute short cycles that are topologically non-trivial. Finally, we describe ongoing work in designing a new algorithm for computing maximum s, t-flows in surface embedded graphs. We begin by describing an algorithm to compute global minimum cuts in edge weighted genus g graphs in gO(g)n log log n time. When the genus is a constant, our algorithm’s running time matches the best time bound known for planar graphs due to La̧cki and Sankowski. In our algorithm, we reduce to the problem of finding a minimum weight separating subgraph in the dual
Author: Kyle Fox
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2302588101