Generalized Networks: Parallel Algorithms and an Empirical Analysis

The objective of this research was to develop and empirically test new simplex-based parallel algorithms for the generalized network optimization problem. One of these algorithms is essentially a “data parallel” method in which each processor executes identical code on a portion of the data. (However, since the data sets are not necessarily disjoint, “locks” are used to ensure exclusive access.) A second algorithm exhibits “control parallelism,” using different processors to simultaneously execute the different subtasks of the simplex method. “Locks” are not needed in this second approach, but, instead, at the beginning of each pivot, an “audit” of the proposed entering arc is performed in order to ensure correctness of the method. These parallel algorithms were implemented on the Sequent Symmetry multiprocessor, empirically tested on a variety of problems produced by two random problem generators, and compared with two leading state-of-the-art serial codes. Good speedups were obtained relative to the ser...