Distributed strong diameter network decomposition: [Extended Abstract]

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

23 Scopus citations

Abstract

For a pair of positive parameters D,x, a partition P of the vertex set V of an n-vertex graph G = (V,E) into disjoint clusters of diameter at most D each is called a (D,x) net- work decomposition, if the supergraph G(P), obtained by contracting each of the clusters of P, can be properly x- colored. The decomposition P is said to be strong (resp., weak) if each of the clusters has strong (resp., weak) diame- ter at most D, i.e., if for every cluster C ϵ P and every two vertices u; v ϵ C, the distance between them in the induced graph G(C) of C (resp., in G) is at most D. Network decomposition is a powerful construct, very use- ful in distributed computing and beyond. It was introduced by Awerbuch et. al. [AGLP89] in the end of the eighties. These authors showed that strong (2O(√log n log log n); 2O(√log n log log n)) network decompositions can be computed in 2O(√log n log log n) distributed time. Their result was improved at the beginning of nineties by Pan- conesi and Srinivasan [PS92], who showed that 2O(√log n log log n) in all the three expressions can be replaced by 2O(√log n). Around the same time Linial and Saks [LS93] devised an ingenious randomized algorithm that constructs weak (O(log n);O(log n)) network decompositions in O(log2 n) time. Awerbuch et. al. [ABCP96] devised a randomized al- gorithm that builds a strong (O(log n);O(log n)) network decomposition in O(log4 n) time, using very large messages and heavy local computations. It was however open till now if strong network decompositions with both parame-ters 2O(√log n) can be constructed in distributed 2O(√log n) time using short messages, or if a result of [LS93] can be strengthened to provide a strong (O(log n);O(log n)) net- work decomposition within O(log2 n) time (even using large messages). In this paper we answer these long-standing open ques- tions in the afirmative, and show that strong (O(log n);O(log n)) network decompositions can be computed in O(log2 n) time. We also present a tradeo between pa- rameters of our network decomposition. Our work is inspired by and relies on the \shifted shortest path approach", due to Blelloch et. al. [BGK+14], and Miller et. al. [MPX13]. These authors developed this approach for PRAM algorithms for padded partitions. We adapt their approach to network decompositions in the distributed model of computation.

Original languageEnglish
Title of host publicationPODC 2016 - Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages211-216
Number of pages6
ISBN (Electronic)9781450339643
DOIs
StatePublished - 25 Jul 2016
Event35th ACM Symposium on Principles of Distributed Computing, PODC 2016 - Chicago, United States
Duration: 25 Jul 201628 Jul 2016

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing
Volume25-28-July-2016

Conference

Conference35th ACM Symposium on Principles of Distributed Computing, PODC 2016
Country/TerritoryUnited States
CityChicago
Period25/07/1628/07/16

Keywords

  • Distributed Model
  • Network decompositions

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

Fingerprint

Dive into the research topics of 'Distributed strong diameter network decomposition: [Extended Abstract]'. Together they form a unique fingerprint.

Cite this