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.ISAAC.2020.25
URN: urn:nbn:de:0030-drops-133693
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13369/
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He, Meng ; Munro, J. Ian ; Nekrich, Yakov ; Wild, Sebastian ; Wu, Kaiyu

Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees

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LIPIcs-ISAAC-2020-25.pdf (0.8 MB)

Abstract

We present the first succinct distance oracles for (unweighted) interval graphs and related classes of graphs, using a novel succinct data structure for ordinal trees that supports the mapping between preorder (i.e., depth-first) ranks and level-order (breadth-first) ranks of nodes in constant time. Our distance oracles for interval graphs also support navigation queries - testing adjacency, computing node degrees, neighborhoods, and shortest paths - all in optimal time. Our technique also yields optimal distance oracles for proper interval graphs (unit-interval graphs) and circular-arc graphs. Our tree data structure supports all operations provided by different approaches in previous work, as well as mapping to and from level-order ranks and retrieving the last (first) internal node before (after) a given node in a level-order traversal, all in constant time.

BibTeX - Entry

@InProceedings{he_et_al:LIPIcs:2020:13369,
  author =	{Meng He and J. Ian Munro and Yakov Nekrich and Sebastian Wild and Kaiyu Wu},
  title =	{{Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13369},
  URN =		{urn:nbn:de:0030-drops-133693},
  doi =		{10.4230/LIPIcs.ISAAC.2020.25},
  annote =	{Keywords: succinct data structures, distance oracles, ordinal tree, level order, breadth-first order, interval graphs, proper interval graphs, succinct graph representation}
}

Keywords: succinct data structures, distance oracles, ordinal tree, level order, breadth-first order, interval graphs, proper interval graphs, succinct graph representation
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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