Drawing Graphs as Spanners

Oswin Aichholzer, Manuel Borrazzo, Prosenjit Bose, Jean Cardinal, Fabrizio Frati*, Pat Morin, Birgit Vogtenhuber

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandBegutachtung

Abstract

We study the problem of embedding graphs in the plane as good geometric spanners. That is, for a graph G, the goal is to construct a straight-line drawing Γ of G in the plane such that, for any two vertices u and v of G, the ratio between the minimum length of any path from u to v and the Euclidean distance between u and v is small. The maximum such ratio, over all pairs of vertices of G, is the spanning ratio of Γ. First, we show that deciding whether a graph admits a straight-line drawing with spanning ratio 1, a proper straight-line drawing with spanning ratio 1, and a planar straight-line drawing with spanning ratio 1 are NP-complete, ∃ R-complete, and linear-time solvable problems, respectively. Second, we prove that, for every ϵ> 0, every (planar) graph admits a proper (resp. planar) straight-line drawing with spanning ratio smaller than 1 + ϵ. Third, we note that our drawings with spanning ratio smaller than 1 + ϵ have large edge-length ratio, that is, the ratio between the lengths of the longest and of the shortest edge is exponential. We show that this is sometimes unavoidable. More generally, we identify having bounded toughness as the criterion that distinguishes graphs that admit straight-line drawings with constant spanning ratio and polynomial edge-length ratio from graphs that do not.

Originalspracheenglisch
TitelGraph-Theoretic Concepts in Computer Science - 46th International Workshop, WG 2020, Revised Selected Papers
Redakteure/-innenIsolde Adler, Haiko Müller
ErscheinungsortLeeds, United Kingdom
Herausgeber (Verlag)Springer International Publishing AG
Seiten310-324
Seitenumfang15
Band12301
ISBN (Print)9783030604394
DOIs
PublikationsstatusElektronische Veröffentlichung vor Drucklegung. - 9 Okt. 2020
Veranstaltung46th International Workshop on Graph-Theoretic Concepts in Computer Science: WG 2020 - Virtuell, Leeds, Großbritannien / Vereinigtes Königreich
Dauer: 24 Juni 202026 Juni 2020

Publikationsreihe

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Band12301 LNCS
ISSN (Print)0302-9743
ISSN (elektronisch)1611-3349

Konferenz

Konferenz46th International Workshop on Graph-Theoretic Concepts in Computer Science
Land/GebietGroßbritannien / Vereinigtes Königreich
OrtVirtuell, Leeds
Zeitraum24/06/2026/06/20

ASJC Scopus subject areas

  • Theoretische Informatik
  • Informatik (insg.)

Fields of Expertise

  • Information, Communication & Computing

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