Efficient Algorithms for RDV graphs
Loading...
Date
2025-05-22
Authors
Advisor
Biedl, Therese
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
In this thesis, we study the maximum matching and minimum dominating set problem in RDV graphs, i.e., graphs that are vertex-intersection graphs of downward paths in a rooted tree. A straightforward implementation of these algorithms would require $O(n+m)$ time. We improve their efficiency by transforming the question about the neighborhood of $v$ into a type of range query amid a set of horizontal and vertical line segments. Our algorithms run in $O(n \log{n})$ time, presuming a $O(n)$-sized intersection representation of the graph is given. In addition, our techniques can also be used to obtain faster algorithms for maximum independent set and perfect $k$-clique packing in RDV graphs.