The network simplex method on a multiprocessor

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Abstract
We compare several implemented approaches to parallelizing the network simplex method on the SEQUENT shared memory multiprocessor. The experiments underscore the importance of parallel pricing and show that specialized processes and single pivots are more efficient than are uniform processes with parallel pivots. We describe the PARNET implementation that combines the best features of the experimental codes. In its least parallel version, PARNET outperforms NETFLO, a standard sequential code, by a factor of 12. The total execution time (including i/o and statistics) for any problem with 5000 nodes and 25,000 arcs taken from a standard set of NETGEN benchmark problems is less than 25 sec wall clock time on the Sequent Symmetry S‐81 using six processors. The incremental speedup is linear up to six processors on the test set and improves with the problem size and the density of the underlying graph. For a problem with 1000 nodes and 500,000 ares, PARNET achieves incremental linear speedup up to 12 processors.