TY - GEN
T1 - Deterministic PRAM approximate shortest paths in polylogarithmic time and slightly super-linear work
AU - Elkin, Michael
AU - Matar, Shaked
N1 - Publisher Copyright:
© 2021 ACM.
PY - 2021/7/6
Y1 - 2021/7/6
N2 - We study a (1+ϵ)-approximate single-source shortest paths (henceforth, (1+ϵ)-SSSP) in n-vertex undirected, weighted graphs in the parallel (PRAM) model of computation. A randomized algorithm with polylogarithmic time and slightly super-linear work Õ(|E|•n^ρ), for an arbitrarily small ρ>0, was given by Cohen (10) more than 25 years ago. Exciting progress on this problem was achieved in recent years (4, 17, 19, 35), culminating in randomized polylogarithmic time and Õ(|E|) work. However, the question of whether there exists a deterministic counterpart of Cohen's algorithm remained wide open. In the current paper we devise the first deterministic polylogarithmic-time algorithm for this fundamental problem, with work Õ(|E|•n^ρ), for an arbitrarily small ρ>0. This result is based on the first efficient deterministic parallel algorithm for building hopsets, which we devise in this paper.
AB - We study a (1+ϵ)-approximate single-source shortest paths (henceforth, (1+ϵ)-SSSP) in n-vertex undirected, weighted graphs in the parallel (PRAM) model of computation. A randomized algorithm with polylogarithmic time and slightly super-linear work Õ(|E|•n^ρ), for an arbitrarily small ρ>0, was given by Cohen (10) more than 25 years ago. Exciting progress on this problem was achieved in recent years (4, 17, 19, 35), culminating in randomized polylogarithmic time and Õ(|E|) work. However, the question of whether there exists a deterministic counterpart of Cohen's algorithm remained wide open. In the current paper we devise the first deterministic polylogarithmic-time algorithm for this fundamental problem, with work Õ(|E|•n^ρ), for an arbitrarily small ρ>0. This result is based on the first efficient deterministic parallel algorithm for building hopsets, which we devise in this paper.
KW - Approximate single source shortest paths
KW - Deterministic
KW - Hopsets
KW - Pram
UR - http://www.scopus.com/inward/record.url?scp=85109535902&partnerID=8YFLogxK
U2 - 10.1145/3409964.3461809
DO - 10.1145/3409964.3461809
M3 - Conference contribution
AN - SCOPUS:85109535902
T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures
SP - 198
EP - 207
BT - SPAA 2021 - Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures
PB - Association for Computing Machinery
T2 - 33rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2021
Y2 - 6 July 2021 through 8 July 2021
ER -