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Locally-Iterative Distributed (Δ+ 1): -Coloring below Szegedy-Vishwanathan Barrier, and Applications to Self-Stabilization and to Restricted-Bandwidth Models by Barenboim, Leonid ;Elkin, Michael ;Goldenberg, Uri is a scholarly article available to read on EtoBox.

What is Locally-Iterative Distributed (Δ+ 1): -Coloring below Szegedy-Vishwanathan Barrier, and Applications to Self-Stabilization and to Restricted-Bandwidth Models about?

We consider graph coloring and related problems in the distributed message-passing model. Locally-iterative algorithms are especially important in this setting. These are algorithms in which each vertex decides about its next color only as a function of the current colors in its 1 -hopneiдhborhood. In STOC'93 Szegedy and Vishwanathan showed that any locally-iterative (∆ + 1)-coloring algorithm requires Ω(∆ log ∆ + log \* n) rounds, unless there exists "a very special type of coloring that can be very efficiently reduced" [39]. No such special coloring has been found since then. This led researchers to believe that Szegedy-Vishwanathan barrier is an inherent limitation for locally-iterative algorithms, and to explore other approaches to the coloring problem [1,2,17,29]. The latter gave rise to faster algorithms, but their heavy machinery which is of non-locally-iterative nature made them far less suitable to various settings. In this paper we obtain the aforementioned special type of coloring. Specifically, we devise a locally-iterative (∆ + 1)-coloring algorithm with running time O(∆ + log \* n), i.e., below Szegedy-Vishwanathan barrier. This demonstrates that this barrier is not a

Author

Barenboim, Leonid ;Elkin, Michael ;Goldenberg, Uri

Publisher

ACM Press

Published

2018

Language

EN