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Succinct Data Structures for Chordal Graphs

Authors J. Ian Munro , Kaiyu Wu

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Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
  • Theory of computation → Data compression
Keywords
  • Succinct Data Structure
  • Chordal Graph

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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

Cite As Get BibTex

J. Ian Munro and Kaiyu Wu. Succinct Data Structures for Chordal Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 67:1-67:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ISAAC.2018.67

Author Details

J. Ian Munro
  • Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada
Kaiyu Wu
  • Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

Funding

This work was supported by NSERC of Canada and the Canada Research Chairs Programme.

References

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