TY - GEN
T1 - Algorithms for coloring reconfiguration under recolorability constraints
AU - Osawa, Hiroki
AU - Suzuki, Akira
AU - Ito, Takehiro
AU - Zhou, Xiao
N1 - Funding Information:
1 Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP17K12636 and JP18H04091, Japan. 2 Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP16K00004 and JP18H04091, Japan. 3 Partially supported by JSPS KAKENHI Grant Number JP16K00003, Japan.
Funding Information:
Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP17K12636 and JP18H04091, Japan. 2 Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP16K00004 and JP18H04091, Japan. 3 Partially supported by JSPS KAKENHI Grant Number JP16K00003, Japan.
Publisher Copyright:
© Hiroki Osawa, Akira Suzuki, Takehiro Ito, and Xiao Zhou; licensed under Creative Commons License CC-BY
PY - 2018/12/1
Y1 - 2018/12/1
N2 - Coloring reconfiguration is one of the most well-studied reconfiguration problems. In the problem, we are given two (vertex-)colorings of a graph using at most k colors, and asked to determine whether there exists a transformation between them by recoloring only a single vertex at a time, while maintaining a k-coloring throughout. It is known that this problem is solvable in linear time for any graph if k ≤ 3, while is PSPACE-complete for a fixed k ≥ 4. In this paper, we further investigate the problem from the viewpoint of recolorability constraints, which forbid some pairs of colors to be recolored directly. More specifically, the recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color, and each edge in R represents a pair of colors that can be recolored directly. In this paper, we give a linear-time algorithm to solve the problem under such a recolorability constraint if R is of maximum degree at most two. In addition, we show that the minimum number of recoloring steps required for a desired transformation can be computed in linear time for a yes-instance. We note that our results generalize the known positive ones for coloring reconfiguration.
AB - Coloring reconfiguration is one of the most well-studied reconfiguration problems. In the problem, we are given two (vertex-)colorings of a graph using at most k colors, and asked to determine whether there exists a transformation between them by recoloring only a single vertex at a time, while maintaining a k-coloring throughout. It is known that this problem is solvable in linear time for any graph if k ≤ 3, while is PSPACE-complete for a fixed k ≥ 4. In this paper, we further investigate the problem from the viewpoint of recolorability constraints, which forbid some pairs of colors to be recolored directly. More specifically, the recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color, and each edge in R represents a pair of colors that can be recolored directly. In this paper, we give a linear-time algorithm to solve the problem under such a recolorability constraint if R is of maximum degree at most two. In addition, we show that the minimum number of recoloring steps required for a desired transformation can be computed in linear time for a yes-instance. We note that our results generalize the known positive ones for coloring reconfiguration.
KW - And phrases combinatorial reconfiguration
KW - Graph algorithm
KW - Graph coloring
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UR - http://www.scopus.com/inward/citedby.url?scp=85063667636&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ISAAC.2018.37
DO - 10.4230/LIPIcs.ISAAC.2018.37
M3 - Conference contribution
AN - SCOPUS:85063667636
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 37:1-37:13
BT - 29th International Symposium on Algorithms and Computation, ISAAC 2018
A2 - Hsu, Wen-Lian
A2 - Lee, Der-Tsai
A2 - Liao, Chung-Shou
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 29th International Symposium on Algorithms and Computation, ISAAC 2018
Y2 - 16 December 2018 through 19 December 2018
ER -