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 |
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| Abstract | 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. |
|---|---|
| AbstractList | We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take poly(loglogn) 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(loglogn) rounds in the near-linear MPC model, where the memory per machine is O~(n) and the total memory is O~(mnρ), 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(loglogn) rounds and allows to query a (1+ϵ)(2k-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+n1+ρ)n1/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(nγ) for a small constant γ<1. All previous algorithms for approximate shortest paths in the near-linear MPC model either required Ω(logn) rounds or had an Ω(logn) 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. 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. 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 . All previous algorithms for approximate shortest paths in the near-linear MPC model either required $$\Omega (\log {n})$$ Ω ( log n ) rounds or had an $$\Omega (\log {n})$$ 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. |
| Author | Matar, Shaked Dory, Michal |
| Author_xml | – sequence: 1 givenname: Michal surname: Dory fullname: Dory, Michal email: mdory@ds.haifa.ac.il organization: Department of Computer Science, University of Haifa – sequence: 2 givenname: Shaked surname: Matar fullname: Matar, Shaked organization: Department of Computer Science, Ben-Gurion University of the Negev |
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| Cites_doi | 10.1109/FOCS.2019.00096 10.1145/3125644 10.1145/3212734.3212743 10.1145/1044731.1044732 10.1145/3382734.3405737 10.1145/2591796.2591805 10.1145/3188745.3188764 10.1145/3519270.3538450 10.1145/3406325.3451136 10.1145/380752.380797 10.1007/s00446-009-0091-7 10.1145/3527213 10.1137/1.9781611976465.110 10.1145/1109557.1109645 10.1137/16M1105815 10.1145/3274651 10.1145/3519270.3538469 10.1145/3293611.3331635 10.1109/FOCS54457.2022.00078 10.1145/1989493.1989505 10.1145/3357713.3384321 10.1145/3465084.3467928 10.1137/1.9781611975482.98 10.1137/1.9781611975482.99 10.1137/20M1366502 10.1145/3357713.3384268 10.1145/3293611.3331609 10.1007/978-3-642-25591-5_39 10.1145/3409964.3461784 10.1137/1.9781611973075.76 10.1145/3293611.3331607 10.1145/1327452.1327492 10.1145/3465084.3467926 10.1145/1272998.1273005 |
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| References | 482_CR17 482_CR18 482_CR15 S Pettie (482_CR35) 2010; 22 482_CR37 482_CR13 482_CR36 482_CR11 482_CR33 482_CR12 482_CR34 A Abboud (482_CR2) 2018; 47 M Zaharia (482_CR39) 2010; 10 482_CR1 482_CR3 482_CR4 482_CR5 M Elkin (482_CR19) 2019; 15 482_CR6 482_CR7 482_CR8 482_CR20 482_CR21 482_CR28 482_CR29 482_CR26 482_CR27 482_CR24 482_CR25 P Beame (482_CR9) 2017; 64 482_CR22 482_CR23 A Czumaj (482_CR10) 2021; 50 M Dory (482_CR16) 2022; 69 T White (482_CR38) 2012 482_CR31 482_CR32 482_CR30 J Dean (482_CR14) 2008; 51 |
| References_xml | – ident: 482_CR28 – ident: 482_CR8 doi: 10.1109/FOCS.2019.00096 – volume: 64 start-page: 40 issue: 6 year: 2017 ident: 482_CR9 publication-title: J. ACM (JACM) doi: 10.1145/3125644 – ident: 482_CR24 doi: 10.1145/3212734.3212743 – ident: 482_CR36 doi: 10.1145/1044731.1044732 – ident: 482_CR25 doi: 10.1145/3382734.3405737 – ident: 482_CR3 doi: 10.1145/2591796.2591805 – ident: 482_CR12 doi: 10.1145/3188745.3188764 – ident: 482_CR23 doi: 10.1145/3519270.3538450 – ident: 482_CR20 – ident: 482_CR34 doi: 10.1145/3406325.3451136 – ident: 482_CR21 doi: 10.1145/380752.380797 – volume: 22 start-page: 147 issue: 3 year: 2010 ident: 482_CR35 publication-title: Distrib. Comput. doi: 10.1007/s00446-009-0091-7 – volume: 69 start-page: 1 issue: 4 year: 2022 ident: 482_CR16 publication-title: J. ACM doi: 10.1145/3527213 – ident: 482_CR7 doi: 10.1137/1.9781611976465.110 – ident: 482_CR37 doi: 10.1145/1109557.1109645 – volume: 47 start-page: 2203 issue: 6 year: 2018 ident: 482_CR2 publication-title: SIAM J. Comput. doi: 10.1137/16M1105815 – volume: 15 start-page: 4:1 issue: 1 year: 2019 ident: 482_CR19 publication-title: ACM Trans. Algorith. doi: 10.1145/3274651 – ident: 482_CR22 doi: 10.1145/3519270.3538469 – ident: 482_CR15 – volume-title: Hadoop: the definitive guide year: 2012 ident: 482_CR38 – ident: 482_CR17 doi: 10.1145/3293611.3331635 – ident: 482_CR30 doi: 10.1109/FOCS54457.2022.00078 – ident: 482_CR33 doi: 10.1145/1989493.1989505 – ident: 482_CR4 doi: 10.1145/3357713.3384321 – ident: 482_CR13 doi: 10.1145/3465084.3467928 – ident: 482_CR1 doi: 10.1137/1.9781611975482.98 – ident: 482_CR27 doi: 10.1137/1.9781611975482.99 – volume: 50 start-page: 1603 issue: 5 year: 2021 ident: 482_CR10 publication-title: SIAM J. Comput. doi: 10.1137/20M1366502 – ident: 482_CR32 doi: 10.1145/3357713.3384268 – volume: 10 start-page: 95 issue: 10–10 year: 2010 ident: 482_CR39 publication-title: HotCloud – ident: 482_CR5 doi: 10.1145/3293611.3331609 – ident: 482_CR26 doi: 10.1007/978-3-642-25591-5_39 – ident: 482_CR6 doi: 10.1145/3409964.3461784 – ident: 482_CR31 doi: 10.1137/1.9781611973075.76 – ident: 482_CR11 doi: 10.1145/3293611.3331607 – volume: 51 start-page: 107 issue: 1 year: 2008 ident: 482_CR14 publication-title: Commun. ACM doi: 10.1145/1327452.1327492 – ident: 482_CR18 doi: 10.1145/3465084.3467926 – ident: 482_CR29 doi: 10.1145/1272998.1273005 |
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| Snippet | We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take
poly
(... We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take... |
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| SubjectTerms | Algorithms Apexes Approximation Computer Communication Networks Computer Hardware Computer Science Computer Systems Organization and Communication Networks Emulators Graph theory Parallel processing Shortest-path problems Sketches Software Engineering/Programming and Operating Systems Theory of Computation |
| Title | Massively parallel algorithms for approximate shortest paths |
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