Density-Dependent Graph Orientation and Coloring in Scalable MPC
This provides improved parallel algorithms for graph processing in scalable MPC, though it appears incremental as it builds on prior work to break a specific complexity barrier.
The paper tackles the problem of graph orientation and coloring in scalable MPC by developing algorithms that run in poly(log log n) rounds, breaking the previous Θ̃(√log n) barrier, and achieving maximum outdegree and number of colors of O(α log log n) where α is the densest subgraph density.
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 $\tildeΘ(\sqrt{\log n})$ 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.