TY - UNPB

T1 - Centralized and Parallel Multi-Source Shortest Paths via Hopsets and Fast Matrix Multiplication.

AU - Elkin, Michael

AU - Neiman, Ofer

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2020

Y1 - 2020

N2 - Consider an undirected weighted graph G=(V,E,w). We study the problem of computing (1+ϵ)-approximate shortest paths for S×V, for a subset S⊆V of |S|=nr sources, for some 00.
In particular, for r≤0.313…, our centralized algorithm computes S×V (1+ϵ)-approximate shortest paths in n2+o(1) time. Our PRAM polylogarithmic-time algorithm has work complexity O(|E|⋅nρ+n2+o(1)), for any arbitrarily small constant ρ>0. Previously existing solutions either require centralized time/parallel work of O(|E|⋅|S|) or provide much weaker approximation guarantees.
In the Congested Clique model, our algorithm solves the problem in polylogarithmic time for |S|=nr sources, for r≤0.655, while previous state-of-the-art algorithms did so only for r≤1/2. Moreover, it improves previous bounds for all r>1/2. For unweighted graphs, the running time is improved further to poly(loglogn).

AB - Consider an undirected weighted graph G=(V,E,w). We study the problem of computing (1+ϵ)-approximate shortest paths for S×V, for a subset S⊆V of |S|=nr sources, for some 00.
In particular, for r≤0.313…, our centralized algorithm computes S×V (1+ϵ)-approximate shortest paths in n2+o(1) time. Our PRAM polylogarithmic-time algorithm has work complexity O(|E|⋅nρ+n2+o(1)), for any arbitrarily small constant ρ>0. Previously existing solutions either require centralized time/parallel work of O(|E|⋅|S|) or provide much weaker approximation guarantees.
In the Congested Clique model, our algorithm solves the problem in polylogarithmic time for |S|=nr sources, for r≤0.655, while previous state-of-the-art algorithms did so only for r≤1/2. Moreover, it improves previous bounds for all r>1/2. For unweighted graphs, the running time is improved further to poly(loglogn).

M3 - ???researchoutput.researchoutputtypes.workingpaper.preprint???

T3 - Arxiv preprint

BT - Centralized and Parallel Multi-Source Shortest Paths via Hopsets and Fast Matrix Multiplication.

ER -