New results on directed edge dominating set

Rémy Belmonte, Tesshu Hanaka, Ioannis Katsikarelis, Eun Jung Kim, Michael Lampis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

We study a family of generalizations of Edge Dominating Set on directed graphs called Directed (p, q)-Edge Dominating Set. In this problem an arc (u, v) is said to dominate itself, as well as all arcs which are at distance at most q from v, or at distance at most p to u. First, we give significantly improved FPT algorithms for the two most important cases of the problem, (0, 1)-dEDS and (1, 1)-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 (p, q)-dEDS is FPT parameterized by p + q + tw, but W-hard parameterized just by tw, where tw is the treewidth of the underlying graph of the input. We then go on to focus on the complexity of the problem on tournaments. Here, we provide a complete classification for every possible fixed value of p, q, which shows that the problem exhibits a surprising behavior, including cases which are in P; cases which are solvable in quasi-polynomial time but not in P; and a single case (p = q = 1) which is NP-hard (under randomized reductions) and cannot be solved in sub-exponential time, under standard assumptions.

Original languageEnglish
Title of host publication43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
EditorsIgor Potapov, James Worrell, Paul Spirakis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770866
DOIs
Publication statusPublished - Aug 1 2018
Externally publishedYes
Event43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 - Liverpool, United Kingdom
Duration: Aug 27 2018Aug 31 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume117
ISSN (Print)1868-8969

Other

Other43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
Country/TerritoryUnited Kingdom
CityLiverpool
Period8/27/188/31/18

All Science Journal Classification (ASJC) codes

  • Software

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