On reconfigurability of target sets

Autor: Naoto Ohsaka
Rok vydání: 2023
Předmět:
Zdroj: Theoretical Computer Science. 942:253-275
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2022.11.036
Popis: We study the problem of deciding reconfigurability of target sets of a graph. Given a graph $G$ with vertex thresholds $\tau$, consider a dynamic process in which vertex $v$ becomes activated once at least $\tau(v)$ of its neighbors are activated. A vertex set $S$ is called a target set if all vertices of $G$ would be activated when initially activating vertices of $S$. In the Target Set Reconfiguration problem, given two target sets $X$ and $Y$ of the same size, we are required to determine whether $X$ can be transformed into $Y$ by repeatedly swapping one vertex in the current set with another vertex not in the current set preserving every intermediate set as a target set. In this paper, we investigate the complexity of Target Set Reconfiguration in restricted cases. On the hardness side, we prove that Target Set Reconfiguration is PSPACE-complete on bipartite planar graphs of degree $3$ and $4$ and of threshold $2$, bipartite $3$-regular graphs and planar $3$-regular graphs of threshold $1$ and $2$, and split graphs, which is in contrast to the fact that a special case called Vertex Cover Reconfiguration is in P for the last graph class. On the positive side, we present a polynomial-time algorithm for Target Set Reconfiguration on graphs of maximum degree $2$ and trees. The latter result can be thought of as a generalization of that for Vertex Cover Reconfiguration.
Comment: 36 pages; changed according to referee suggestions; to appear in Theoretical Computer Science
Databáze: OpenAIRE
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