Load-Balancing Spatially Located Computations using Rectangular Partitions

TL;DR

This paper addresses the complex problem of partitioning spatial workloads into rectangles to balance load across processors, introducing new algorithms and heuristics that outperform existing methods in simulation.

Contribution

It introduces m-way jagged partitions, develops optimal algorithms for these and hierarchical partitions, and provides new heuristics with performance analysis.

Findings

New algorithms achieve better load balance than existing methods.

Two-phase algorithm offers flexible tradeoffs between computation time and load balance.

Simulation results validate the effectiveness of the proposed algorithms.

Abstract

Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles, such that the load of the most loaded rectangle (processor) is minimized. Since finding the optimal arbitrary rectangle-based partition is an NP-hard problem, we investigate particular classes of solutions: rectilinear, jagged and hierarchical. We present a new class of solutions called m-way jagged partitions, propose new optimal algorithms for m-way jagged partitions and hierarchical partitions, propose new heuristic algorithms, and provide worst case performance analyses for some existing and new heuristics. Moreover, the algorithms are tested in simulation on a wide set of instances. Results show that two of the algorithms we introduce lead to a much better load balance than the state-of-the-art algorithms. We also show how to design a two-phase algorithm that reaches different time/quality tradeoff.