Year: 2025
Type: article
Abstract: We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take $$\textrm{poly}(\log {\log {n}})$$ poly ( log log n ) rounds in the near-linear memory MPC model. Our results are for unweighted undirected graphs with n vertices and m edges. Our first contribution is a $$(1+\epsilon )$$ ( 1 + ϵ ) -approximation algorithm for Single-Source Shortest Paths (SSSP) that takes $$\textrm{poly}(\log {\log {n}})$$ poly ( log log n ) rounds in the near-linear MPC model, where the memory per machine is $$\tilde{O}(n)$$ O ~ ( n ) and the total memory is $$\tilde{O}(mn^{\rho })$$ O ~ ( m n ρ ) , where $$\rho $$ ρ is a small constant. Our second contribution is a distance oracle that allows to approximate the distance between any pair of vertices. The distance oracle is constructed in $$\textrm{poly}(\log {\log {n}})$$ poly ( log log n ) rounds and allows to query a $$(1+\epsilon )(2k-1)$$ ( 1 + ϵ ) ( 2 k - 1 ) -approximate distance between any pair of vertices u and v in O(1) additional rounds. The algorithm is for the near-linear memory MPC model with total memory of size $$\tilde{O}((m+n^{1+\rho })n^{1/k})$$ O ~ ( ( m + n 1 + ρ ) n 1 / k ) , where $$\rho $$ ρ is a small constant. While our algorithms are for the near-linear MPC model, in fact they only use one machine with $$\tilde{O}(n)$$ O ~ ( n ) memory, where the rest of machines can have sublinear memory of size $$O(n^{\gamma })$$ O ( n γ ) for a small constant $$\gamma < 1$$ γ < 1
Source: Distributed Computing
Authors: Michal Dory, Shaked Matar
Institutions: University of Haifa, Ben-Gurion University of the Negev
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,490
Funder: University of Haifa
OpenAlex ID: W4409713909