Density-Dependent Graph Orientation and Coloring in Scalable MPC
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3732772.3733501.pdf
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606.47 KB
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388db8cc7716dafff146b2fa4d6b5393
Author(s)
Ghaffari, Mohsen
Grunau, Christoph
Date Issued
June 13, 2025
Publisher
ACM|ACM Symposium on Principles of Distributed Computing
Citation
Mohsen Ghaffari and Christoph Grunau. 2025. Density-Dependent Graph Orientation and Coloring in Scalable MPC. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC '25). Association for Computing Machinery, New York, NY, USA, 349–359.
Version
Final published version
Abstract
This paper presents massively parallel computation (MPC) algorithms in the strongly sublinear memory regime (aka, scalable MPC) for orienting and coloring graphs as a function of its subgraph density. Our algorithms run in poly(log log n) rounds and compute an orientation of the edges with maximum outdegree O (α log log n) as well as a coloring of the vertices with O (α log log n) colors. Here, α denotes the density of the densest subgraph. Our algorithm's round complexity is notable because it breaks the [EQUATION] barrier, which applied to the previously best known density-dependent orientation algorithm [Ghaffari, Lattanzi, and Mitrovic ICML'19] and is common to many other scalable MPC algorithms.
Description
PODC ’25, Huatulco, Mexico
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3732772.3733501
