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Dynamic algorithms for graph coloring
KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.ORCID iD: 0000-0003-4468-2675
2018 (English)In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for 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
Association for Computing Machinery , 2018. p. 1-20
Keywords [en]
Clustering algorithms, Coloring, Deterministic algorithms, Dynamic algorithm, Dynamic settings, Edge-coloring algorithms, Graph colorings, Insertions and deletions, Linear-time algorithms, Randomized Algorithms, Graph theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-227491DOI: 10.1137/1.9781611975031.1Scopus ID: 2-s2.0-85045565161ISBN: 9781611975031 OAI: oai:DiVA.org:kth-227491DiVA, id: diva2:1206171
Conference
29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, 7 January 2018 through 10 January 2018
Note

Conference code: 133646; Export Date: 9 May 2018; Conference Paper; CODEN: PAAAF. QC 20180516

Available from: 2018-05-16 Created: 2018-05-16 Last updated: 2018-05-16Bibliographically approved

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Na Nongkai, Danupon

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  • apa
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Output format
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