Finding maximum matchings in RDV graphs efficiently
Computational Geometry
2024-06-07 v1 Data Structures and Algorithms
Abstract
In this paper, we study the maximum matching problem in RDV graphs, i.e., graphs that are vertex-intersection graphs of downward paths in a rooted tree. We show that this problem can be reduced to a problem of testing (repeatedly) whether a vertical segment intersects one of a dynamically changing set of horizontal segments, which in turn reduces to an orthogonal ray shooting query. Using a suitable data structure, we can therefore find a maximum matching in time (presuming a linear-sized representation of the graph is given), i.e., without even looking at all edges.
Cite
@article{arxiv.2406.03632,
title = {Finding maximum matchings in RDV graphs efficiently},
author = {Therese Biedl and Prashant Gokhale},
journal= {arXiv preprint arXiv:2406.03632},
year = {2024}
}