Finding maximum matchings in RDV graphs efficiently
<|reference_start|>Finding maximum matchings in RDV graphs efficiently: 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 $O(n\log n)$ time (presuming a linear-sized representation of the graph is given), i.e., without even looking at all edges.<|reference_end|>
@article{biedl2024finding,
    title={Finding maximum matchings in RDV graphs efficiently},
    author={Therese Biedl, Prashant Gokhale},
    journal={arXiv preprint arXiv:2406.03632},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03632},
    primaryClass={cs.CG cs.DS}
}