Fast partial distance estimation and applications

Christoph Lenzen, Boaz Patt-Shamir

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

Abstract

We study approximate distributed solutions to the weighted all-pairs-shortest-paths (APSP) problem in the CONGEST model. We obtain the following results. A deterministic (1 + ε)-approximation to APSP with running time O(ε-2nlogn) rounds. The best previously known algorithm was randomized and slower by a (log n) factor. In many cases, routing schemes involve relabeling, i.e., assigning new names to nodes and that are used in distance and routing queries. It is known that relabeling is necessary to achieve running times of o(n/ log n). In the relabeling model, we obtain the following results. A randomized O(k)-approximation to APSP, for any inateger k > 1, running in O(n1/2+1/k + D) rounds, where D is the hop diameter of the network. This algorithm simplifies the best previously known result and reduces its approximaation ratio from O(k log k) to O(k). Also, the new algorithm uses O(logn)-bit labels, which is asymptotically optimal. A randomized O(k)-approximation to APSP, for any integer k > 1, running in time O((nD)1/2 • n1/k + D) and producing compact routing tables of size labels consist of O(k log n) bits. This improves on the apaproximation ratio of (k2) for tables of that size achieved by the best previously known algorithm, which terminates faster, in O(n1/2+1/k + D) rounds. In addition, we improve on the time complexity of the best known deterministic algorithm for distributed approximate Steiner forest.

Original languageEnglish
Title of host publicationPODC 2015 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages153-162
Number of pages10
ISBN (Electronic)9781450336178
DOIs
StatePublished - 21 Jul 2015
EventACM Symposium on Principles of Distributed Computing, PODC 2015 - Donostia-San Sebastian, Spain
Duration: 21 Jul 201523 Jul 2015

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing
Volume2015-July

Conference

ConferenceACM Symposium on Principles of Distributed Computing, PODC 2015
Country/TerritorySpain
CityDonostia-San Sebastian
Period21/07/1523/07/15

Keywords

  • Congest model
  • Routing table construction
  • Source detection
  • Steiner forests
  • Weighted all-pairs shortest paths

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