On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets

Lokshtanov, Daniel and Mouawad, Amer E. and Panolan, Fahad and Siebertz, Sebastian (2020) On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets. In: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020), 14 December 2020through 18 December 2020, Virtual, Hong Kong.

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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 Kd,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 + `, 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. © Daniel Lokshtanov, Amer E. Mouawad, Fahad Panolan, and Sebastian Siebertz;

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