Upper Domination: Towards a Dichotomy Through Boundary Properties

Upper Domination: Towards a Dichotomy Through Boundary Properties 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

Upper Domination: Towards a Dichotomy Through Boundary Properties

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-017-0346-9
Publisher site
See Article on Publisher Site

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.

Journal

AlgorithmicaSpringer Journals

Published: Jul 14, 2017

References

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