eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-12-14
13:1
13:13
10.4230/LIPIcs.ISAAC.2022.13
article
Computation of Cycle Bases in Surface Embedded Graphs
Fox, Kyle
1
Stanley, Thomas
2
University of Texas at Dallas, Richardson, TX, USA
Unaffiliated, Dallas, TX, USA
We present an O(n³ g²log g + m) + Õ(n^{ω + 1}) time deterministic algorithm to find the minimum cycle basis of a directed graph embedded on an orientable surface of genus g. This result improves upon the previous fastest known running time of O(m³n + m²n² log n) applicable to general directed graphs.
While an O(n^ω + 2^{2g}n² + m) time deterministic algorithm was known for undirected graphs, the use of the underlying field ℚ in the directed case (as opposed to ℤ₂ for the undirected case) presents extra challenges. It turns out that some of our new observations are useful for both variants of the problem, so we present an O(n^ω + n² g² log g + m) time deterministic algorithm for undirected graphs as well.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol248-isaac2022/LIPIcs.ISAAC.2022.13/LIPIcs.ISAAC.2022.13.pdf
cycle basis
surface embedded graphs
homology