Weighted Additive Spanners

Reyan Ahmed, Greg Bodwin, Faryad Darabi Sahneh, Stephen Kobourov, Richard Spence

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A spanner of a graph G is a subgraph H that approximately preserves shortest path distances in G. Spanners are commonly applied to compress computation on metric spaces corresponding to weighted input graphs. Classic spanner constructions can seamlessly handle edge weights, so long as error is measured multiplicatively. In this work, we investigate whether one can similarly extend constructions of spanners with purely additive error to weighted graphs. These extensions are not immediate, due to a key lemma about the size of shortest path neighborhoods that fails for weighted graphs. Despite this, we recover a suitable amortized version, which lets us prove direct extensions of classic + 2 and + 4 unweighted spanners (both all-pairs and pairwise) to + 2 W and + 4 W weighted spanners, where W is the maximum edge weight. Specifically, we show that a weighted graph G contains all-pairs (pairwise) + 2 W and + 4 W weighted spanners of size O(n3 / 2) and O(n7 / 5) (O(np1 / 3) and O(np2 / 7) ) respectively. For a technical reason, the + 6 unweighted spanner becomes a + 8 W weighted spanner; closing this error gap is an interesting remaining open problem. That is, we show that G contains all-pairs (pairwise) + 8 W weighted spanners of size O(n4 / 3) (O(np1 / 4) ).

Original languageEnglish (US)
Title of host publicationGraph-Theoretic Concepts in Computer Science - 46th International Workshop, WG 2020, Revised Selected Papers
EditorsIsolde Adler, Haiko Müller
PublisherSpringer Science and Business Media Deutschland GmbH
Pages401-413
Number of pages13
ISBN (Print)9783030604394
DOIs
StatePublished - 2020
Event46th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2020 - Leeds, United Kingdom
Duration: Jun 24 2020Jun 26 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12301 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference46th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2020
CountryUnited Kingdom
CityLeeds
Period6/24/206/26/20

Keywords

  • Additive spanner
  • Pairwise spanner
  • Shortest-path neighborhood

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Weighted Additive Spanners'. Together they form a unique fingerprint.

Cite this