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

Authors Meng He , J. Ian Munro , Yakov Nekrich, Sebastian Wild , Kaiyu Wu

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Author Details

Meng He
  • Dalhousie University, Halifax, Canada
J. Ian Munro
  • University of Waterloo, Canada
Yakov Nekrich
  • Michigan Tech, Houghton, MI, USA
Sebastian Wild
  • University of Liverpool, UK
Kaiyu Wu
  • University of Waterloo, Canada

Funding

  • Munro, J. Ian: NSERC and the Canada Research Chairs Programme.

Cite AsGet BibTex

Meng He, J. Ian Munro, Yakov Nekrich, Sebastian Wild, and Kaiyu Wu. Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ISAAC.2020.25

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Data compression
Keywords
  • succinct data structures
  • distance oracles
  • ordinal tree
  • level order
  • breadth-first order
  • interval graphs
  • proper interval graphs
  • succinct graph representation

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