Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-Stabilization

Leonid Barenboim, Gal Oren

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

6 Scopus citations

Abstract

In the distributed backup-placement problem [9] each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in which each node is selected just by one neighbor. Previous (approximate) solutions for backup placement are non-trivial, even for simple graph topologies, such as dense graphs [5]. In this paper we devise an algorithm for dense graph topologies, including unit disk graphs, unit ball graphs, line graphs, graphs with bounded diversity, and many more. Our algorithm requires just one round, and is as simple as the following operation. Consider a circular list of neighborhood IDs, sorted in an ascending order, and select the ID that is next to the selecting vertex ID. Surprisingly, such a simple one-round strategy turns out to be very efficient for backup placement computation in dense networks. Not only that it improves the number of rounds of the solution, but also the approximation ratio is improved by a multiplicative factor of at least 2. Our new algorithm has several interesting implications. In particular, it gives rise to a (2 + ε)-approximation to maximum matching within O(log n) rounds in dense networks. The resulting algorithm is very simple as well, in sharp contrast to previous algorithms that compute such a solution within this running time. Moreover, these algorithms are applicable to a narrower graph family than our algorithm. For the same graph family, the best previously-known result has O(log ∆ + log n) running time [4]. Another interesting implication is the possibility to execute our backup placement algorithm as-is in the self-stabilizing setting. This makes it possible to simplify and improve other algorithms for the self-stabilizing setting, by employing helpful properties of backup placement.

Original languageEnglish
Title of host publication3rd SIAM Symposium on Simplicity in Algorithms, SOSA 2020
EditorsMartin Farach-Colton, Inge Li Gortz
PublisherSociety for Industrial and Applied Mathematics Publications
Pages99-105
Number of pages7
ISBN (Electronic)9781713807377
StatePublished - 2020
Externally publishedYes
Event3rd SIAM Symposium on Simplicity in Algorithms, SOSA 2020 - Salt Lake City, United States
Duration: 6 Jan 20207 Jan 2020

Publication series

Name3rd SIAM Symposium on Simplicity in Algorithms, SOSA 2020

Conference

Conference3rd SIAM Symposium on Simplicity in Algorithms, SOSA 2020
Country/TerritoryUnited States
CitySalt Lake City
Period6/01/207/01/20

Bibliographical note

Publisher Copyright:
© 2020 by SIAM.

Fingerprint

Dive into the research topics of 'Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-Stabilization'. Together they form a unique fingerprint.

Cite this