δ-Greedy t-spanner

Gali Bar On, Paz Carmi

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

Abstract

We introduce a new geometric spanner, δ-Greedy, whose construction is based on a generalization of the known Path-Greedy and Gap-Greedy spanners. The δ-Greedy spanner combines the most desirable properties of geometric spanners both in theory and in practice. More specifically, it has the same theoretical and practical properties as the Path-Greedy spanner: a natural definition, small degree, linear number of edges, low weight, and strong (1+ε)-spanner for every ε > 0. The δ-Greedy algorithm is an improvement over the Path-Greedy algorithm with respect to the number of shortest path queries and hence with respect to its construction time. We show how to construct such a spanner for a set of n points in the plane in O(n2 log n) time. The δ-Greedy spanner has an additional parameter, δ, which indicates how close it is to the Path-Greedy spanner on the account of the number of shortest path queries. For δ = t the output spanner is identical to the Path-Greedy spanner, while the number of shortest path queries is, in practice, linear. Finally, we show that for a set of n points placed independently at random in a unit square the expected construction time of the δ-Greedy algorithm is O(n log n). Our analysis indicates that the δ-Greedy spanner gives the best results among the known spanners of expected O(n log n) time for random point sets. Moreover, analysis implies that by setting δ = t, the δ-Greedy algorithm provides a spanner identical to the Path-Greedy spanner in expected O(n log n) time.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
EditorsFaith Ellen, Antonina Kolokolova, Jorg-Rudiger Sack
PublisherSpringer Verlag
Pages85-96
Number of pages12
ISBN (Print)9783319621265
DOIs
StatePublished - 1 Jan 2017
Event15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada
Duration: 31 Jul 20172 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10389 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Symposium on Algorithms and Data Structures, WADS 2017
Country/TerritoryCanada
CitySt. John’s
Period31/07/172/08/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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