Upper Domination: Towards a Dichotomy Through Boundary Properties

Hassan M. AbouEisha, Shahid Hussain, Vadim Lozin, Jérôme Monnot, Bernard Ries, Viktor Zamaraev

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

An upper dominating set in a graph is a minimal dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in finitely defined classes of graphs and conjecture that the problem admits a complexity dichotomy in this family. A helpful tool to study the complexity of an algorithmic problem is the notion of boundary classes. However, none of such classes has been identified so far for the upper dominating set problem. We discover the first boundary class for this problem and prove the dichotomy for monogenic classes.
Original languageEnglish (US)
Pages (from-to)2799-2817
Number of pages19
JournalAlgorithmica
Volume80
Issue number10
DOIs
StatePublished - Jul 14 2017

Fingerprint

Dive into the research topics of 'Upper Domination: Towards a Dichotomy Through Boundary Properties'. Together they form a unique fingerprint.

Cite this