Approximating maximum integral multiflows on bounded genus graphs
Data Structures and Algorithms
2021-12-14 v2 Computational Geometry
Discrete Mathematics
Abstract
We devise the first constant-factor approximation algorithm for finding an integral multi-commodity flow of maximum total value for instances where the supply graph together with the demand edges can be embedded on an orientable surface of bounded genus. This extends recent results for planar instances. Our techniques include an uncrossing algorithm, which is significantly more difficult than in the planar case, a partition of the cycles in the support of an LP solution into free homotopy classes, and a new rounding procedure for freely homotopic non-separating cycles.
Keywords
Cite
@article{arxiv.2005.00575,
title = {Approximating maximum integral multiflows on bounded genus graphs},
author = {Chien-chung Huang and Mathieu Mari and Claire Mathieu and Jens Vygen},
journal= {arXiv preprint arXiv:2005.00575},
year = {2021}
}