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arXiv · 1805.01208

Balanced k-means for Parallel Geometric Partitioning

Moritz von Looz·Charilaos Tzovas·Henning Meyerhenke
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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.

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Moritz von Looz, Charilaos Tzovas, Henning Meyerhenke. 2018-05-03. Balanced k-means for Parallel Geometric Partitioning. https://arxiv.org/abs/1805.01208

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