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Dynamic Algorithms for Graph Coloring
Univ Warwick, Dept Comp Sci, Coventry, W Midlands, England..
Dartmouth Coll, Dept Comp Sci, Hanover, NH 03755 USA..
Univ Vienna, Fac Comp Sci, Vienna, Austria..
KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.ORCID iD: 0000-0003-4468-2675
2018 (English)In: SODA'18: PROCEEDINGS OF THE TWENTY-NINTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, ASSOC COMPUTING MACHINERY , 2018, p. 1-20Conference paper, Published paper (Refereed)
Abstract [en]

We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for ( δ + 1)vertex coloring and (2 δ 1)edge coloring in a graph with maximum degree δ. It is natural to ask if we can efficiently maintain such colorings in the dynamic setting as well. We get the following three results. (1) We present a randomized algorithm which maintains a ( δ+1)-vertex coloring with O(log δ) expected amortized update time. (2) We present a deterministic algorithm which maintains a (1 + o(1)) δ-vertex coloring with O(polylog δ) amortized update time. (3) We present a simple, deterministic algorithm which maintains a (2 δ)edge coloring with O(log δ) worst-case update time. This improves the recent O( δ)-edge coloring algorithm with Õ ( p δ) worst-case update time [4].

Place, publisher, year, edition, pages
ASSOC COMPUTING MACHINERY , 2018. p. 1-20
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-260237DOI: 10.1137/1.9781611975031.1ISI: 000483921200001Scopus ID: 2-s2.0-85045565161OAI: oai:DiVA.org:kth-260237DiVA, id: diva2:1355332
Conference
The Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, Louisiana — January 07 - 10, 2018
Note

QC 20190927

Available from: 2019-09-27 Created: 2019-09-27 Last updated: 2019-10-14Bibliographically approved

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Na Nongkai, Danupon

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