Correlating Theory and Practice in Finding Clubs and Plexes
Data Structures and Algorithms
2022-12-16 v1
Abstract
Finding large "cliquish" subgraphs is a classic NP-hard graph problem. In this work, we focus on finding maximum -clubs and -plexes, i.e., graphs of diameter and graphs where each vertex is adjacent to all but vertices. Preprocessing based on Turing kernelization is a standard tool to tackle these problems, especially on sparse graphs. We provide a new parameterized analysis for the Turing kernelization and demonstrate their usefulness in practice. Moreover, we provide evidence that the new theoretical bounds indeed better explain the observed running times than the existing theoretical running time bounds. To this end, we suggest a general method to compare how well theoretical running time bounds fit to measured running times.
Cite
@article{arxiv.2212.07533,
title = {Correlating Theory and Practice in Finding Clubs and Plexes},
author = {Aleksander Figiel and Tomohiro Koana and André Nichterlein and Niklas Wünsche},
journal= {arXiv preprint arXiv:2212.07533},
year = {2022}
}