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New Algorithms for Mixed Dominating Set

Authors Louis Dublois, Michael Lampis, Vangelis Th. Paschos



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Author Details

Louis Dublois
  • Université Paris-Dauphine, PSL University, CNRS, LAMSADE, Paris, France
Michael Lampis
  • Université Paris-Dauphine, PSL University, CNRS, LAMSADE, Paris, France
Vangelis Th. Paschos
  • Université Paris-Dauphine, PSL University, CNRS, LAMSADE, Paris, France

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Louis Dublois, Michael Lampis, and Vangelis Th. Paschos. New Algorithms for Mixed Dominating Set. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 9:1-9:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.IPEC.2020.9

Abstract

A mixed dominating set is a set of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for MDS, resolving some open questions. In particular, we settle the problem’s complexity parameterized by treewidth and pathwidth by giving an algorithm running in time O^*(5^{tw}) (improving the current best O^*(6^{tw})), and a lower bound showing that our algorithm cannot be improved under the SETH, even if parameterized by pathwidth (improving a lower bound of O^*((2-ε)^{pw})). Furthermore, by using a simple but so far overlooked observation on the structure of minimal solutions, we obtain branching algorithms which improve the best known FPT algorithm for this problem, from O^*(4.172^k) to O^*(3.510^k), and the best known exact algorithm, from O^*(2ⁿ) and exponential space, to O^*(1.912ⁿ) and polynomial space.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • FPT Algorithms
  • Exact Algorithms
  • Mixed Domination

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