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Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time

Author Hanlin Ren

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ACM Subject Classification
  • Theory of computation → Shortest paths
  • Theory of computation → Data structures design and analysis
Keywords
  • Graph theory
  • Failure-prone structures

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Abstract

We consider the problem of building Distance Sensitivity Oracles (DSOs). Given a directed graph G = (V, E) with edge weights in {1, 2, … , M}, we need to preprocess it into a data structure, and answer the following queries: given vertices u,v,x ∈ V, output the length of the shortest path from u to v that does not go through x. Our main result is a simple DSO with Õ(n^2.7233 M²) preprocessing time and O(1) query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to Õ(n^2.6865 M²). Our algorithms are randomized with correct probability ≥ 1-1/n^c, for a constant c that can be made arbitrarily large. Previously, there is a DSO with Õ(n^2.8729 M) preprocessing time and polylog(n) query time [Chechik and Cohen, STOC'20].
At the core of our DSO is the following observation from [Bernstein and Karger, STOC'09]: if there is a DSO with preprocessing time P and query time Q, then we can construct a DSO with preprocessing time P+Õ(Mn²)⋅ Q and query time O(1). (Here Õ(⋅) hides polylog(n) factors.)

Cite As Get BibTex

Hanlin Ren. Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ESA.2020.79

Author Details

Hanlin Ren
  • Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

Acknowledgements

I would like to thank Zihao Li for introducing this problem to me, and Ran Duan and Yong Gu for helpful discussions. I would also like to thank Hongxun Wu for reading and commenting an early draft version of this paper, and pointing out the issue with non-unique shortest paths. I am also grateful to the anonymous referees of ESA for their helpful comments that improves the presentation of this work.

References

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