Parallel Breadth-First Search and Exact Shortest Paths and Stronger Notions for Approximate Distances

10/28/2022
by   Václav Rozhoň, et al.
0

We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One application is the first work-efficient parallel algorithm for computing exact single-source shortest paths graphs – resolving a major open problem in parallel computing. Given a source vertex in a directed graph with polynomially-bounded nonnegative integer lengths, the algorithm computes an exact shortest path tree in m log^O(1) n work and n^1/2+o(1) depth. Previously, no parallel algorithm improving the trivial linear depths of Dijkstra's algorithm without significantly increasing the work was known, even for the case of undirected and unweighted graphs (i.e., for computing a BFS-tree). Our main result is a black-box transformation that uses log^O(1) n standard approximate distance computations to produce approximate distances which also satisfy the subtractive triangle inequality (up to a (1+ε) factor) and even induce an exact shortest path tree in a graph with only slightly perturbed edge lengths. These strengthened approximations are algorithmically significantly more powerful and overcome well-known and often encountered barriers for using approximate distances. In directed graphs they can even be boosted to exact distances. This results in a black-box transformation of any (parallel or distributed) algorithm for approximate shortest paths in directed graphs into an algorithm computing exact distances at essentially no cost. Applying this to the recent breakthroughs of Fineman et al. for compute approximate SSSP-distances via approximate hopsets gives new parallel and distributed algorithm for exact shortest paths.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/11/2019

Efficient Construction of Directed Hopsets and Parallel Approximate Shortest Paths

The approximate single-source shortest-path problem is as follows: given...
research
12/25/2017

Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of...
research
07/15/2020

Directed Shortest Paths via Approximate Cost Balancing

We present an O(nm) algorithm for all-pairs shortest paths computations ...
research
07/16/2022

A Parallel Privacy-Preserving Shortest Path Protocol from a Path Algebra Problem

In this paper, we present a secure multiparty computation (SMC) protocol...
research
02/12/2020

Shortest path distance approximation using deep learning techniques

Computing shortest path distances between nodes lies at the heart of man...
research
07/10/2022

Closing the Gap Between Directed Hopsets and Shortcut Sets

For an n-vertex directed graph G = (V,E), a β-shortcut set H is a set of...
research
07/28/2021

(1+ε)-Approximate Shortest Paths in Dynamic Streams

Computing approximate shortest paths in the dynamic streaming setting is...

Please sign up or login with your details

Forgot password? Click here to reset