Massively parallel algorithms for approximate shortest paths
We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take 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 fir...
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| Vydáno v: | Distributed computing Ročník 38; číslo 2; s. 131 - 162 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2025
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-2770, 1432-0452 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take
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
+
ϵ
)
-approximation algorithm for Single-Source Shortest Paths (SSSP) that takes
poly
(
log
log
n
)
rounds in the near-linear MPC model, where the memory per machine is
O
~
(
n
)
and the total memory is
O
~
(
m
n
ρ
)
, where
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
poly
(
log
log
n
)
rounds and allows to query a
(
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
O
~
(
(
m
+
n
1
+
ρ
)
n
1
/
k
)
, where
ρ
is a small constant. While our algorithms are for the near-linear MPC model, in fact they only use one machine with
O
~
(
n
)
memory, where the rest of machines can have sublinear memory of size
O
(
n
γ
)
for a small constant
γ
<
1
. All previous algorithms for approximate shortest paths in the near-linear MPC model either required
Ω
(
log
n
)
rounds or had an
Ω
(
log
n
)
approximation. Our approach is based on fast construction of near-additive emulators, limited-scale hopsets and limited-scale distance sketches that are tailored for the MPC model. While our end-results are for the near-linear MPC model, many of the tools we construct such as hopsets and emulators are constructed in the more restricted sublinear MPC model. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0178-2770 1432-0452 |
| DOI: | 10.1007/s00446-025-00482-y |