Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Approximate Distance Oracles with Improved Query Time

  • Christian Wulff-NilsenEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_568-1

Years and Authors of Summarized Original Work

2013; Wulff-Nilsen

Problem Definition

This problem is concerned with obtaining a compact data structure capable of efficiently reporting approximate shortest path distance queries in a given undirected edge-weighted graph G = (V, E). If the query time is independent (or nearly independent) of the size of G, we refer to the data structure as an approximate distance oracle for G. For vertices u and v in G, we denote by dG(u, v) the shortest path distance between u and v in G. For a given stretch parameter δ ≥ 1, we call the oracle δ-approximate if for all vertices u and v in G, \(d_{G}(u,v) \leq \tilde{ d}_{G}(u,v) \leq \delta d_{G}(u,v)\)


Approximate distance oracle Shortest paths Graphs Query time 
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Recommended Reading

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    Chechik S (2014) Approximate distance oracles with constant query time. In: STOC, New York, pp 654–663Google Scholar
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    Erdős P (1964) Extremal problems in graph theory. In: Theory of graphs and its applications (Proceedings of the symposium on smolenice, 1963). Czechoslovak Academy of Sciences, Prague, pp 29–36Google Scholar
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    Mendel M, Naor A (2007) Ramsey partitions and proximity data structures. J Eur Math Soc 9(2):253–275. See also FOCS’06Google Scholar
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    Thorup M, Zwick U (2005) Approximate distance oracles. J Assoc Comput Mach 52:1–24zbMATHMathSciNetCrossRefGoogle Scholar
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    Wulff-Nilsen C (2013) Approximate distance oracles with improved query time. In: Proceedings of the 24th ACM-SIAM symposium on discrete algorithms (SODA), New Orleans, pp 202–208Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark