License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.24
URN: urn:nbn:de:0030-drops-124313
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12431/
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Cen, Ruoxu ; Duan, Ran ; Gu, Yong

Roundtrip Spanners with (2k-1) Stretch

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LIPIcs-ICALP-2020-24.pdf (0.5 MB)

Abstract

A roundtrip spanner of a directed graph G is a subgraph of G preserving roundtrip distances approximately for all pairs of vertices. Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected graphs. For a directed graph with real edge weights in [1,W], we first propose a new deterministic algorithm that constructs a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log (nW)) edges for every integer k > 1, then remove the dependence of size on W to give a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log n) edges. While keeping the edge size small, our result improves the previous 2k+ε stretch roundtrip spanners in directed graphs [Roditty, Thorup, Zwick'02; Zhu, Lam'18], and almost matches the undirected (2k-1)-spanner with O(n^(1+1/k)) edges [Althöfer et al. '93] when k is a constant, which is optimal under Erdös conjecture.

BibTeX - Entry

@InProceedings{cen_et_al:LIPIcs:2020:12431,
  author =	{Ruoxu Cen and Ran Duan and Yong Gu},
  title =	{{Roundtrip Spanners with (2k-1) Stretch}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{24:1--24:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12431},
  URN =		{urn:nbn:de:0030-drops-124313},
  doi =		{10.4230/LIPIcs.ICALP.2020.24},
  annote =	{Keywords: Graph theory, Deterministic algorithm, Roundtrip spanners}
}

Keywords: Graph theory, Deterministic algorithm, Roundtrip spanners
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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