Shortest Beer Path Queries in Interval Graphs

Rathish Das, Meng He, Eitan Kondratovsky, J. Ian Munro, Anurag Murty Naredla, Kaiyu Wu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

Our interest is in paths between pairs of vertices that go through at least one of a subset of the vertices known as beer vertices. Such a path is called a beer path, and the beer distance between two vertices is the length of the shortest beer path. We show that we can represent unweighted interval graphs using 2n log n + O(n) + O(|B| log n) bits where |B| is the number of beer vertices. This data structure answers beer distance queries in O(logε n) time for any constant ε > 0 and shortest beer path queries in O(logε n + d) time, where d is the beer distance between the two nodes. We also show that proper interval graphs may be represented using 3n + o(n) bits to support beer distance queries in O(f(n) log n) time for any f(n) ∈ ω(1) and shortest beer path queries in O(d) time. All of these results also have time-space trade-offs. Lastly we show that the information theoretic lower bound for beer proper interval graphs is very close to the space of our structure, namely log(4 + 2 3)n - o(n) (or about 2.9n) bits.

Original languageEnglish
Title of host publication33rd International Symposium on Algorithms and Computation, ISAAC 2022
EditorsSang Won Bae, Heejin Park
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772587
DOIs
StatePublished - 1 Dec 2022
Externally publishedYes
Event33rd International Symposium on Algorithms and Computation, ISAAC 2022 - Virtual, Online, Korea, Republic of
Duration: 19 Dec 202221 Dec 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume248
ISSN (Print)1868-8969

Conference

Conference33rd International Symposium on Algorithms and Computation, ISAAC 2022
Country/TerritoryKorea, Republic of
CityVirtual, Online
Period19/12/2221/12/22

Bibliographical note

Publisher Copyright:
© Rathish Das, Meng He, Eitan Kondratovsky, J. Ian Munro, Anurag Murty Naredla, and Kaiyu Wu.

Keywords

  • Beer Path
  • Interval Graph

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