Data partitioning schemes for the parallel implementation of the revised simplex algorithm for LP problems

The parallel implementation of the revised simplex algorithm (RSA) using eta-factorization holds the promise of significant improvement in the execution time by virtue of the existence of a high degree of parallelism in the computation within an iteration of the algorithm. However, the scheme employed to partition key data structures in a distributed memory parallel processor has a great impact on the achievable performance. The paper explores the trade-offs between block-row and block-column partitioning schemes for the matrix of constraint coefficients vis-a-vis the communication overheads and granularity of parallel computations. The results of an approximate analysis of the compute-communication balance are compared with measurements from practical implementation of the partitioning schemes on C-DAC's PARAM 8000 distributed memory parallel processor.<>