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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85024370811&partnerID=8YFLogxK

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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 -