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.2018.67
URN: urn:nbn:de:0030-drops-100153
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10015/
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Munro, J. Ian ; Wu, Kaiyu

Succinct Data Structures for Chordal Graphs

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LIPIcs-ISAAC-2018-67.pdf (0.4 MB)

Abstract

We study the problem of approximate shortest path queries in chordal graphs and give a n log n + o(n log n) bit data structure to answer the approximate distance query to within an additive constant of 1 in O(1) time.
We study the problem of succinctly storing a static chordal graph to answer adjacency, degree, neighbourhood and shortest path queries. Let G be a chordal graph with n vertices. We design a data structure using the information theoretic minimal n^2/4 + o(n^2) bits of space to support the queries:
- whether two vertices u,v are adjacent in time f(n) for any f(n) in omega(1).
- the degree of a vertex in O(1) time.
- the vertices adjacent to u in (f(n))^2 time per neighbour
- the length of the shortest path from u to v in O(nf(n)) time

BibTeX - Entry

@InProceedings{munro_et_al:LIPIcs:2018:10015,
  author =	{J. Ian Munro and Kaiyu Wu},
  title =	{{Succinct Data Structures for Chordal Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{67:1--67:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10015},
  URN =		{urn:nbn:de:0030-drops-100153},
  doi =		{10.4230/LIPIcs.ISAAC.2018.67},
  annote =	{Keywords: Succinct Data Structure, Chordal Graph}
}

Keywords: Succinct Data Structure, Chordal Graph
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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