Near-Additive Spanners in Low Polynomial Deterministic CONGEST Time

Michael Elkin, Shaked Matar

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

6 Scopus citations

Abstract

Given a pair of parameters α ≥ 1, β ≥ 0, a subgraph G′ = (V,H) of an n-vertex unweighted undirected graph G = (V, E) is called an (α, β)-spanner if for every pair u,v ϵ V of vertices, we have dG′ (u,v) ≤ αdG(u,v) + β. If β = 0 the spanner is called a multiplicative α-spanner, and if α = 1 + ϵ, for an arbitrarily small ϵ > 0, the spanner is said to be near-additive. Graph spanners [5, 36] are a fundamental and extremely wellstudied combinatorial construct, with a multitude of applications in distributed computing and in other areas. Near-additive spanners, introduced in [27], preserve large distances much more faithfully than the more traditional multiplicative spanners. Also, recent lower bounds [1] ruled out the existence of arbitrarily sparse purely additive spanners (i.e., spanners with α = 1), and therefore showed that essentially near-additive spanners provide the best approximation of distances that one can hope for. Numerous distributed algorithms, for constructing sparse nearadditive spanners, were devised in [17, 20, 25, 28, 40]. In particular, there are now known efficient randomized algorithms in the CONGEST model that construct such spanners [25], and also there are efficient deterministic algorithms in the LOCAL model [17]. However, the only known deterministic CONGEST-model algorithm for the problem [20] requires super-linear time in n. In this paper, we remedy the situation and devise an efficient deterministic CONGEST-model algorithm for constructing arbitrarily sparse near-additive spanners. The running time of our algorithm is low polynomial, i.e., roughly O(β · np ), where p > 0 is an arbitrarily small positive constant that affects the additive term β. In general, the parameters of our new algorithm and of the resulting spanner are at the same ballpark as the respective parameters of the state-of-the-art randomized algorithm due to [25].

Original languageEnglish
Title of host publicationPODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages531-540
Number of pages10
ISBN (Electronic)9781450362177
DOIs
StatePublished - 16 Jul 2019
Event38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada
Duration: 29 Jul 20192 Aug 2019

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference38th ACM Symposium on Principles of Distributed Computing, PODC 2019
Country/TerritoryCanada
CityToronto
Period29/07/192/08/19

Keywords

  • Congest
  • Deterministic
  • Spanners

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