Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time

07/22/2020
by   Hanlin Ren, et al.
0

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∈ V and a failed vertex or edge f∈ (V∪ E), output the length of the shortest path from u to v that does not go through f. Our main result is a simple DSO with Õ(n^2.7233M) preprocessing time and O(1) query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to Õ(n^2.6865M). The preprocessing algorithm is 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^2.8729M) 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(n^2)· Q and query time O(1). (Here Õ(·) hides polylog(n) factors.)

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/17/2021

Constructing a Distance Sensitivity Oracle in O(n^2.5794M) Time

We continue the study of distance sensitivity oracles (DSOs). Given a di...
research
06/05/2023

Efficient exact enumeration of single-source geodesics on a non-convex polyhedron

In this paper, we consider enumeration of geodesics on a polyhedron, whe...
research
08/18/2022

Customizable Hub Labeling: Properties and Algorithms

Hub Labeling (HL) is one of the state-of-the-art preprocessing-based tec...
research
07/25/2022

Simple O(1) Query Algorithm for Level Ancestors

This note describes a very simple O(1) query time algorithm for finding ...
research
04/22/2022

Parameterized Sensitivity Oracles and Dynamic Algorithms using Exterior Algebras

We design the first efficient sensitivity oracles and dynamic algorithms...
research
04/06/2017

Landmark Guided Probabilistic Roadmap Queries

A landmark based heuristic is investigated for reducing query phase run-...
research
02/22/2019

A time-distance trade-off for GDD with preprocessing---Instantiating the DLW heuristic

For 0 ≤α≤ 1/2, we show an algorithm that does the following. Given appro...

Please sign up or login with your details

Forgot password? Click here to reset