Abstract
We explore the question how well we can color graphs in distributed models, especially in graph classes for which Δ + 1-colorings provide no approximation guarantees. We particularly focus on interval graphs.
In the \(\mathcal{LOCAL}\) model, we give an algorithm that computes a constant factor approximation to the coloring problem on interval graphs in O(log* n) rounds, which is best possible. The result holds also for the \(\mathcal{CONGEST}\) model when the representation of the nodes as intervals is given.
We then consider restricted beep models, where communication is restricted to the aggregate acknowledgment of whether a node’s attempted coloring succeeds. We apply an algorithm designed for the SINR model and give a simplified proof of a O(logn)-approximation. We show a nearly matching Ω(logn / loglogn)-approximation lower bound in that model.
Both authors are supported by Icelandic Research Fund grant-of-excellence no. 120032011.
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Halldórsson, M.M., Konrad, C. (2014). Distributed Algorithms for Coloring Interval Graphs. In: Kuhn, F. (eds) Distributed Computing. DISC 2014. Lecture Notes in Computer Science, vol 8784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45174-8_31
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DOI: https://doi.org/10.1007/978-3-662-45174-8_31
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