The efficient parallel solution of generalized network flow problems

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5897719

Clark, R H

This thesis is principally concerned with the discussion of two efficient parallel codes for the generalized network flow problem. Both of the codes are variants of the primal simplex method for generalized networks, and both were implemented by the author on a shared memory multiprocessor, the Sequent Symmetry S81. PGRNET, the first code, exploits parallelism in the pivoting and the pricing operation. Parallel pivoting is made possible by the disjoint nature of the basis graphs. Two processors may execute pivots simultaneously if the pivots involve updating different basis components (quasi-trees), and locking is used to ensure that processors have exclusive access to quasi-trees during the execution of a pivot. The second code, TPGRNET, exploits parallelism in the pricing operation and overlaps pricing and pivoting. Pivots are executed serially by a host processor, pivot arcs are selected from a collection of shared candidate lists by a selecting processor, and all remaining processors compute reduced costs in parallel and store pivot-eligible arcs in the shared candidate lists. TPGRNET is more efficient than PGRNET for problems having only a few quasi-trees in an optimal basis. Computational results for PGRNET for transportation problems with 30,000 nodes and over 320,000 arcs are given, and speedups over GRNET2, a state-of-the-art serial program range from 3.8 to 11.1 on 19 processors. Results for TPGRNET are given for large scale transportation and transshipment problems, and speedups over GRNET2 range from 2.6 to 8.8. A hybrid algorithm that can invoke PGRNET or TPGRNET is briefly described, and results are given, with speedups ranging from 6.1 to 13.2. Two test problems with more than a million variables were solved by PGRNET with speedups ranging from 7.0 to 11.0.

• Research Organization: Wisconsin Univ., Madison, WI (USA)
• OSTI ID: 5897719
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
ARRAY PROCESSORS
COMPUTER NETWORKS
DATA-FLOW PROCESSING
MATHEMATICAL LOGIC
PARALLEL PROCESSING
PROGRAMMING