Density-Dependent Graph Orientation and Coloring in Scalable MPC

2025-06-13

ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing

AI Summary

This work proposes the first algorithm for edge orientation and vertex coloring in the scalable massively parallel computation (MPC) model that achieves a round complexity of poly(log log n), breaking through the previous Ω̃(√log n)-round barrier. Operating under strong sublinear memory constraints, the algorithm outputs an orientation with maximum out-degree and a coloring using O(α log log n) colors, where α denotes the graph’s arboricity—a standard measure of subgraph density. Both bounds significantly improve upon existing methods, offering a substantial reduction in communication rounds while maintaining high solution quality.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

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.

Problem

• graph orientation
• graph coloring
• subgraph density
• scalable MPC
• massively parallel computation

Innovation

• scalable MPC
• graph orientation
• graph coloring
• subgraph density
• poly(log log n) rounds