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Closing the Gap: Minimum Space Optimal Time Distance Labeling Scheme for Interval Graphs

Authors Meng He , Kaiyu Wu

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Author Details

Meng He
  • Faculty of Computer Science, Dalhousie University, Halifax, Canada
Kaiyu Wu
  • Faculty of Computer Science, Dalhousie University, Halifax, Canada

Funding

This work was supported by NSERC.

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Meng He and Kaiyu Wu. Closing the Gap: Minimum Space Optimal Time Distance Labeling Scheme for Interval Graphs. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CPM.2024.17

Abstract

We present a distance labeling scheme for an interval graph on n vertices that uses at most 3lg n + lg lg n + O(1) bits per vertex to answer distance queries, which ask for the distance between two given vertices, in constant time. Our labeling scheme improves the distance labeling scheme of Gavoille and Paul for connected interval graphs which uses at most 5lg n + O(1) bits per vertex to achieve constant query time. Our improved space cost matches a lower bound proven by Gavoille and Paul within additive lower order terms and is thus optimal. Based on this scheme, we further design a 6lg n + 2lg lg n +O(1) bit distance labeling scheme for circular-arc graphs, with constant distance query time, which improves the 10lg n + O(1) bit distance labeling scheme of Gavoille and Paul.
We give a n/2 + O(lg^ 2n) bit labeling scheme for chordal graphs which answers distance queries in O(1) time. The best known lower bound is n/4 - o(n) bits.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Data compression
Keywords
  • Distance Labeling
  • Interval Graph
  • Circular-Arc Graph
  • Chordal Graph

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