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On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets

Authors Daniel Lokshtanov, Amer E. Mouawad, Fahad Panolan, Sebastian Siebertz

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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • reconfiguration
  • parameterized complexity
  • connected dominating set
  • graph structure theory

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Abstract

In a reconfiguration version of a decision problem 𝒬 the input is an instance of 𝒬 and two feasible solutions S and T. The objective is to determine whether there exists a step-by-step transformation between S and T such that all intermediate steps also constitute feasible solutions. In this work, we study the parameterized complexity of the Connected Dominating Set Reconfiguration problem (CDS-R). It was shown in previous work that the Dominating Set Reconfiguration problem (DS-R) parameterized by k, the maximum allowed size of a dominating set in a reconfiguration sequence, is fixed-parameter tractable on all graphs that exclude a biclique K_{d,d} as a subgraph, for some constant d ≥ 1. We show that the additional connectivity constraint makes the problem much harder, namely, that CDS-R is W[1]-hard parameterized by k+𝓁, the maximum allowed size of a dominating set plus the length of the reconfiguration sequence, already on 5-degenerate graphs. On the positive side, we show that CDS-R parameterized by k is fixed-parameter tractable, and in fact admits a polynomial kernel on planar graphs.

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Daniel Lokshtanov, Amer E. Mouawad, Fahad Panolan, and Sebastian Siebertz. On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.IPEC.2020.24

Author Details

Daniel Lokshtanov
  • University of California Santa Barbara, CA, USA
Amer E. Mouawad
  • Department of Computer Science, American University of Beirut, Lebanon
Fahad Panolan
  • Department of Computer Science and Engineering, IIT Hyderabad, India
Sebastian Siebertz
  • University of Bremen, Germany

Funding

  • Mouawad, Amer E.: The second author is supported by URB project "A theory of change through the lens of reconfiguration".

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