research-article

Distributed Construction of Light Networks

Authors:

Arnold Filtser,

Ofer NeimanAuthors Info & Claims

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

Pages 483 - 492

https://doi.org/10.1145/3382734.3405701

Published: 31 July 2020 Publication History

Abstract

A t-spanner H of a weighted graph G = (V, E, w) is a subgraph that approximates all pairwise distances up to a factor of t. The lightness of H is defined as the ratio between the weight of H to that of the minimum spanning tree. An (α, β)-Shallow Light Tree (SLT) is a tree of lightness β, that approximates all distances from a designated root vertex up to a factor of α. A long line of works resulted in efficient algorithms that produce (nearly) optimal light spanners and SLTs.

Some of the most notable algorithmic applications of light spanners and SLTs are in distributed settings. Surprisingly, so far there are no known efficient distributed algorithms for constructing these objects in general graphs. In this paper we devise efficient distributed algorithms in the CONGEST model for constructing light spanners and SLTs, with near optimal parameters. Specifically, for any k ≥ 1 and 0 < ∈ < 1, we show a (2k − 1) · (1 + ∈)-spanner with lightness O(k·n¹/^k) can be built in [EQUATION] rounds (where n = |V| and D is the hop-diameter of G). In addition, for any α > 1 we provide an [EQUATION] rounds. The running times of our algorithms cannot be substantially improved.

We also consider spanners for the family of doubling graphs, and devise a [EQUATION] rounds algorithm in the CONGEST model that computes a (1 + ∈)-spanner with lightness (log n)/∈^O(1). As a stepping stone, which is interesting in its own right, we first develop a distributed algorithm for constructing nets (for arbitrary weighted graphs), generalizing previous algorithms that worked only for unweighted graphs.

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Cited By

Filtser ALe HLeonardi SGupta A(2022)Locality-sensitive orderings and applications to reliable spannersProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520042(1066-1079)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520042
Eppstein DKhodabandeh HAgrawal KLee I(2022)Brief Announcement: Distributed Lightweight Spanner Construction for Unit Ball Graphs in Doubling MetricsProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538553(57-59)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538553
Kitamura NKitagawa HOtachi YIzumi T(2021)Low-congestion shortcut and graph parametersDistributed Computing10.1007/s00446-021-00401-xOnline publication date: 28-Aug-2021
https://doi.org/10.1007/s00446-021-00401-x

Index Terms

Distributed Construction of Light Networks
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Routing and network design problems
    2. Distributed algorithms

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cover image ACM Conferences

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

July 2020

539 pages

ISBN:9781450375825

DOI:10.1145/3382734

General Chair:
Yuval Emek
Technion, Israel
,
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Christian Cachin
University of Bern, Switzerland

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Published: 31 July 2020

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Cited By

Filtser ALe HLeonardi SGupta A(2022)Locality-sensitive orderings and applications to reliable spannersProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520042(1066-1079)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520042
Eppstein DKhodabandeh HAgrawal KLee I(2022)Brief Announcement: Distributed Lightweight Spanner Construction for Unit Ball Graphs in Doubling MetricsProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538553(57-59)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538553
Kitamura NKitagawa HOtachi YIzumi T(2021)Low-congestion shortcut and graph parametersDistributed Computing10.1007/s00446-021-00401-xOnline publication date: 28-Aug-2021
https://doi.org/10.1007/s00446-021-00401-x

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