Balanced k-means for Parallel Geometric Partitioning

TL;DR

This paper introduces Geographer, a scalable balanced k-means-based mesh partitioning algorithm that outperforms existing geometric methods in communication efficiency and scales effectively to very large meshes and high process counts.

Contribution

The paper presents a novel scalable balanced k-means algorithm with space-filling curve initialization, forming the core of the Geographer partitioner, improving mesh partitioning quality and scalability.

Findings

Geographer achieves lower communication volume than state-of-the-art methods.

It scales well on large meshes and high process counts.

Partitioning a billion-vertex mesh takes only a few seconds.

Abstract

Mesh partitioning is an indispensable tool for efficient parallel numerical simulations. Its goal is to minimize communication between the processes of a simulation while achieving load balance. Established graph-based partitioning tools yield a high solution quality; however, their scalability is limited. Geometric approaches usually scale better, but their solution quality may be unsatisfactory for `non-trivial' mesh topologies. In this paper, we present a scalable version of $k$-means that is adapted to yield balanced clusters. Balanced $k$-means constitutes the core of our new partitioning algorithm Geographer. Bootstrapping of initial centers is performed with space-filling curves, leading to fast convergence of the subsequent balanced k-means algorithm. Our experiments with up to 16384 MPI processes on numerous benchmark meshes show the following: (i) Geographer produces partitions with a lower communication volume than state-of-the-art geometric partitioners from the Zoltan package; (ii) Geographer scales well on large inputs; (iii) a Delaunay mesh with a few billion vertices and edges can be partitioned in a few seconds.