Parallel Derandomization for Coloring (Abstract)
Pages 31 - 32
Abstract
Graph coloring problems are among the most fundamental problems in parallel and distributed computing, and have been studied extensively in both settings. In this context, designing efficient deterministic algorithms for these problems has been found particularly challenging.
In this work we consider this challenge, and design a novel framework for derandomizing algorithms for coloring-type problems in the Massively Parallel Computation (MPC) model with sublinear space. We give an application of this framework by showing that a recent (degree+1)-list coloring algorithm by Halldorsson et al. (STOC'22) in the LOCAL model of distributed computation can be translated to the MPC model and efficiently derandomized. Our algorithm runs in O(łog łog łog n) rounds, which matches the complexity of the state of the art algorithm for the (Δ + 1)-coloring problem.
References
[1]
Leonid Barenboim and Michael Elkin. 2013. Distributed Graph Coloring: Fundamentals and Recent Developments. Morgan & Claypool Publishers.
[2]
Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. 2019. An Exponential Separation between Randomized and Deterministic Complexity in the LOCAL Model. SIAM J. Comput., Vol. 48, 1 (2019), 122--143.
[3]
Yi-Jun Chang, Manuela Fischer, Mohsen Ghaffari, Jara Uitto, and Yufan Zheng. 2019. The Complexity of $(Δ 1)$ Coloring in Congested Clique, Massively Parallel Computation, and Centralized Local Computation. In ¶roc 38th ¶ODC (PODC'19). 471--480.
[4]
Sam Coy and Artur Czumaj. 2022. Deterministic Massively Parallel Connectivity. In ¶roc 52th STOC (STOC'22). 162--175.
[5]
Sam Coy, Artur Czumaj, Peter Davies, and Gopinath Mishra. 2023. Parallel Derandomization for Coloring. arxiv: 2302.04378 [cs.DS]
[6]
Sam Coy, Artur Czumaj, Peter Davies, and Gopinath Mishra. 2024. Parallel Derandomization for Coloring. In To appear in the 38th IEEE International Parallel & Distributed Processing Symposium, IPDPS.
[7]
Artur Czumaj, Peter Davies, and Merav Parter. 2021. Component Stability in Low-space Massively Parallel Computation. In ¶roc 40th ¶ODC (PODC'21). 481--491.
[8]
Artur Czumaj, Peter Davies, and Merav Parter. 2021. Improved Deterministic (Δ1$) Coloring in Low-Space MPC. In ¶roc 40th ¶ODC (PODC'21). 469--479.
[9]
Artur Czumaj, Peter Davies, and Merav Parter. 2021. Simple, Deterministic, Constant-Round Coloring in Congested Clique and MPC. SIAM J. Comput., Vol. 50, 5 (2021), 1603--1626.
[10]
Mohsen Ghaffari, Fabian Kuhn, and Jara Uitto. 2019. Conditional Hardness Results for Massively Parallel Computation from Distributed Lower Bounds. In ¶roc 60th FOCS (FOCS'19). 1650--1663.
[11]
Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. 2010. A Model of Computation for MapReduce. In ¶roc 21st SODA (SODA'10). 938--948.
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- Parallel Derandomization for Coloring (Abstract)
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Published: 26 July 2024
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SPAA '24: 36th ACM Symposium on Parallelism in Algorithms and Architectures
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