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Constant-Time Dynamic (Δ+1)-Coloring

Authors Monika Henzinger , Pan Peng

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Author Details

Monika Henzinger
  • University of Vienna, Faculty of Computer Science, Vienna, Austria
Pan Peng
  • Department of Computer Science, University of Sheffield, Sheffield, UK

Funding

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement no. 340506.

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Monika Henzinger and Pan Peng. Constant-Time Dynamic (Δ+1)-Coloring. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 53:1-53:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.STACS.2020.53

Abstract

We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Δ+1)-vertex coloring of a graph with maximum degree at most Δ. This improves upon the previous O(log Δ)-time algorithm by Bhattacharya et al. (SODA 2018). Our algorithm uses an approach based on assigning random ranks to vertices and does not need to maintain a hierarchical graph decomposition. We show that our result does not only have optimal running time, but is also optimal in the sense that already deciding whether a Δ-coloring exists in a dynamically changing graph with maximum degree at most Δ takes Ω(log n) time per operation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Dynamic graph algorithms
  • Graph coloring
  • Random sampling

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