Finding maximum matchings in RDV graphs efficiently
DOI:
https://doi.org/10.57717/cgt.v5i2.72Abstract
In this paper, we study the maximum matching problem in RDV graphs, i.e., 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 horizontal segment intersects one of a dynamically changing set of vertical segments, which in turn reduces to a range minimum query. Using a suitable data structure, we can therefore find a maximum matching in O(n log n) time (presuming a linear-sized representation of the graph is given), i.e., without even looking at all edges.
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2026 Therese Biedl, Prashant Gokhale
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
