eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-26
79:1
79:13
10.4230/LIPIcs.ESA.2020.79
article
Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time
Ren, Hanlin
1
Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
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.)
https://drops.dagstuhl.de/storage/00lipics/lipics-vol173-esa2020/LIPIcs.ESA.2020.79/LIPIcs.ESA.2020.79.pdf
Graph theory
Failure-prone structures