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Title: Computation of Cycle Bases in Surface Embedded Graphs
We present an O(n³ g² log 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(m³ n + m² n² 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.  more » « less
Award ID(s):
1942597
NSF-PAR ID:
10437228
Author(s) / Creator(s):
;
Editor(s):
Bae, Sang Won; Park, Heejin
Date Published:
Journal Name:
33rd International Symposium on Algorithms and Computation
Page Range / eLocation ID:
13:1–13:13
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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