TY - GEN
T1 - Dynamic graph coloring
AU - Barba, Luis
AU - Cardinal, Jean
AU - Korman, Matias
AU - Langerman, Stefan
AU - Van Renssen, André
AU - Roeloffzen, Marcel
AU - Verdonschot, Sander
N1 - Funding Information:
M. K. was partially supported by MEXT KAKENHI grant Nos. 12H00855, and 17K12635. A. v. R. and M. R. were supported by JST ERATO Grant Number JPMJER1305, Japan. L.B. was supported by the ETH Postdoctoral Fellowship. S. V. was partially supported by NSERC and the Carleton-Fields postdoctoral award.
Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used. For any d > 0, the first algorithm maintains a proper O(CdN1/d)-coloring while recoloring at most O(d) vertices per update, where C and N are the maximum chromatic number and maximum number of vertices, respectively. The second algorithm reverses the trade-off, maintaining an O(Cd)-coloring with O(dN1/d) recolorings per update. We also present a lower bound, showing that any algorithm that maintains a c-coloring of a 2-colorable graph on N vertices must recolor at least Ω(N 2/ c(c−1)) vertices per update, for any constant c ≥ 2.
AB - In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used. For any d > 0, the first algorithm maintains a proper O(CdN1/d)-coloring while recoloring at most O(d) vertices per update, where C and N are the maximum chromatic number and maximum number of vertices, respectively. The second algorithm reverses the trade-off, maintaining an O(Cd)-coloring with O(dN1/d) recolorings per update. We also present a lower bound, showing that any algorithm that maintains a c-coloring of a 2-colorable graph on N vertices must recolor at least Ω(N 2/ c(c−1)) vertices per update, for any constant c ≥ 2.
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U2 - 10.1007/978-3-319-62127-2_9
DO - 10.1007/978-3-319-62127-2_9
M3 - Conference contribution
AN - SCOPUS:85024370811
SN - 9783319621265
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 97
EP - 108
BT - Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
A2 - Ellen, Faith
A2 - Kolokolova, Antonina
A2 - Sack, Jorg-Rudiger
PB - Springer Verlag
T2 - 15th International Symposium on Algorithms and Data Structures, WADS 2017
Y2 - 31 July 2017 through 2 August 2017
ER -