New Results on Directed Edge Dominating Set
R\'emy Belmonte, Tesshu Hanaka, Ioannis Katsikarelis, Eun Jung Kim,, Michael Lampis

TL;DR
This paper introduces improved fixed-parameter tractable algorithms, polynomial kernels, and approximation algorithms for directed edge dominating set problems, and provides a comprehensive complexity classification on tournaments.
Contribution
It significantly advances algorithmic solutions and complexity understanding for the directed edge dominating set problem, especially on tournaments and specific parameterizations.
Findings
Improved FPT algorithms for (0,1)-dEDS and (1,1)-dEDS.
Polynomial kernels and constant-factor approximations for key cases.
Complete complexity classification for directed edge dominating set on tournaments.
Abstract
We study a family of generalizations of Edge Dominating Set on directed graphs called Directed -Edge Dominating Set. In this problem an arc is said to dominate itself, as well as all arcs which are at distance at most from , or at distance at most to . First, we give significantly improved FPT algorithms for the two most important cases of the problem, -dEDS and -dEDS (that correspond to versions of Dominating Set on line graphs), as well as polynomial kernels. We also improve the best-known approximation for these cases from logarithmic to constant. In addition, we show that -dEDS is FPT parameterized by , but W-hard parameterized by (even if the size of the optimal is added as a second parameter), where is the treewidth of the underlying graph of the input. We then go on to focus on the complexity of the problem…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems
