TY - GEN
T1 - Algorithms for Coloring Reconfiguration Under Recolorability Digraphs
AU - Fujii, Soichiro
AU - Iwamasa, Yuni
AU - Kimura, Kei
AU - Suzuki, Akira
N1 - Funding Information:
Funding Soichiro Fujii: Partially supported by JST, ERATO Grant Number JPMJER1603 (HASUO Metamathematics for Systems Design Project) and JSPS Overseas Research Fellowships. Yuni Iwamasa: Partially supported by JSPS KAKENHI Grant Numbers JP20K23323, JP20H05795, 22K17854, Japan. Kei Kimura: Partially supported by JSPS KAKENHI Grant Numbers JP19K22841, JP21K17700, Japan. Akira Suzuki: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP20K11666, JP20H05794, Japan.
Publisher Copyright:
© Soichiro Fujii, Yuni Iwamasa, Kei Kimura, and Akira Suzuki.
PY - 2022/12/1
Y1 - 2022/12/1
N2 - In the k-Recoloring problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper k-coloring. This problem is known to be solvable in polynomial time if k ≤ 3, and is PSPACE-complete if k ≥ 4. In this paper, we consider a (directed) recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of a digraph -→R, whose vertices correspond to the colors and whose arcs represent the pairs of colors that can be recolored directly. We provide algorithms for the problem based on the structure of recolorability constraints -→R, showing that the problem is solvable in linear time when -→R is a directed cycle or is in a class of multitrees.
AB - In the k-Recoloring problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper k-coloring. This problem is known to be solvable in polynomial time if k ≤ 3, and is PSPACE-complete if k ≥ 4. In this paper, we consider a (directed) recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of a digraph -→R, whose vertices correspond to the colors and whose arcs represent the pairs of colors that can be recolored directly. We provide algorithms for the problem based on the structure of recolorability constraints -→R, showing that the problem is solvable in linear time when -→R is a directed cycle or is in a class of multitrees.
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U2 - 10.4230/LIPIcs.ISAAC.2022.4
DO - 10.4230/LIPIcs.ISAAC.2022.4
M3 - Conference contribution
AN - SCOPUS:85144237364
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 33rd International Symposium on Algorithms and Computation, ISAAC 2022
A2 - Bae, Sang Won
A2 - Park, Heejin
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 33rd International Symposium on Algorithms and Computation, ISAAC 2022
Y2 - 19 December 2022 through 21 December 2022
ER -