Distributed symmetry-breaking algorithms for congested cliques

Leonid Barenboim, Victor Khazanov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The Congested Clique is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an n-vertex graph in which any pair of vertices can communicate one with another by transmitting O(log n) bits in each round. Various problems have been studied in this setting, but for some of them the best-known results are those for general networks. For other problems, the results for Congested Cliques are better than on general networks, but still incur significant dependency on the number of vertices n. Hence the performance of these algorithms may become poor on large cliques, even though their diameter is just 1. In this paper we devise significantly improved algorithms for various symmetry-breaking problems, such as forests-decompositions, vertex-colorings, and maximal independent set. We analyze the running time of our algorithms as a function of the arboricity a of a clique subgraph that is given as input. The arboricity is always smaller than the number of vertices n in the subgraph, and for many families of graphs it is significantly smaller. In particular, trees, planar graphs, graphs with constant genus, and many other graphs have bounded arboricity, but unbounded size. We obtain O(a)-forest-decomposition algorithm with O(log a) time that improves the previously-known O(log n) time, O(a2+ε)-coloring in O(log*n) time that improves upon an O(log n)-time algorithm, O(a)-coloring in (aε)-time that improves upon several previous algorithms, and a maximal independent set algorithm with O(√a}) time that improves at least quadratically upon the state-of-the-art for small and moderate values of a. Those results are achieved using several techniques. First, we produce a forest decomposition with a helpful structure called H-partition within O(log a) rounds. In general graphs this structure requires Θ(log n) time, but in Congested Cliques we are able to compute it faster. We employ this structure in conjunction with partitioning techniques that allow us to solve various symmetry-breaking problems efficiently.

Original languageEnglish
Title of host publicationComputer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings
EditorsVladimir V. Podolskii, Fedor V. Fomin
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319905297
StatePublished - 2018
Event13th International Computer Science Symposium in Russia, CSR 2018 - Moscow, Russian Federation
Duration: 6 Jun 201810 Jun 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10846 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Computer Science Symposium in Russia, CSR 2018
Country/TerritoryRussian Federation

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.


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