On the Massively Parallel Solution of The Assignment Problem

Abstract

In this paper we discuss the design, implementation and effectiveness of massively parallel algorithms for the solution of large-scale assignment problems. In particular, we study the auction algorithm of Bertsekas, an algorithm based on the method of multipliers of Hestenes and Powell, and an algorithm based on the alternating direction method of multipliers of Eckstein. We discuss alternative approaches to the massively parallel implementation of the auction algorithm, including Jacobi, Gauss-Seidel and a hybrid scheme. The hybrid scheme, in particular, exploits two different levels of parallelism and an efficient way of communicating the data between them without the need to perform general router operations across the hypercube network. We then study the performance of massively parallel implementations of the two methods of multipliers. Implementations are carried out on the Connection Machine CM-2, and the algorithms are evaluated empirically with the solution of large scale problems. The hybrid scheme significantly outperforms all of the other methods and gives the best computational results to date for a massively parallel solution to this problem.