Affiliation:
1. University of Warwick, UK
2. IST Austria, Klosterneuburg, Austria
3. Weizmann Institute of Science, Rehovot, Israel
Abstract
The Massively Parallel Computation (MPC) model is an emerging model that distills core aspects of distributed and parallel computation, developed as a tool to solve combinatorial (typically graph) problems in systems of many machines with limited space.
Recent work has focused on the regime in which machines have sublinear (in
n
, the number of nodes in the input graph) space, with randomized algorithms presented for the fundamental problems of Maximal Matching and Maximal Independent Set. However, there have been no prior corresponding
deterministic
algorithms.
A major challenge underlying the sublinear space setting is that the local space of each machine might be too small to store all edges incident to a single node. This poses a considerable obstacle compared to classical models in which each node is assumed to know and have easy access to its incident edges. To overcome this barrier, we introduce a new
graph sparsification
technique that
deterministically
computes a low-degree subgraph, with the additional property that solving the problem on this subgraph provides significant progress towards solving the problem for the original input graph.
Using this framework to derandomize the well-known algorithm of Luby [SICOMP’86], we obtain
O
(log Δ + log log
n
)-round
deterministic
MPC algorithms for solving the problems of
Maximal Matching
and
Maximal Independent Set
with
O
(
n
ɛ
) space on each machine for any constant ɛ > 0. These algorithms also run in
O
(log Δ) rounds in the closely related model of CONGESTED CLIQUE, improving upon the state-of-the-art bound of
O
(log
2
Δ) rounds by Censor-Hillel et al. [DISC’17].
Funder
Centre for Discrete Mathematics and its Applications (DIMAP), by a Weizmann-UK Making Connections
Centre for Discrete Mathematics and its Applications
Weizmann-UK Making Connections Grant, by IBM Faculty Award, and by Engineering and Physical Sciences Research Council
European Union's Horizon 2020 research and innovation programme
Engineering and Physical Sciences Research Council
Weizmann-UK Making Connections Grant and Minerva
Marie Skłodowska-Curie
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
6 articles.
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1. Fast Dynamic Programming in Trees in the MPC Model;Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures;2023-06-17
2. Deterministic Massively Parallel Symmetry Breaking for Sparse Graphs;Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures;2023-06-17
3. Superfast coloring in CONGEST via efficient color sampling;Theoretical Computer Science;2023-02
4. Massively Parallel Computation in a Heterogeneous Regime;Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing;2022-07-20
5. Deterministic graph coloring in the streaming model;Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing;2022-06-09