Parallel Simplex for Large Pure Network Problems: Computational Testing and Sources of Speedup

This pa per re ports on a new par al lel im ple men ta tion of the pri mal sim plex method for mini mum cost net work flow prob lems, that de com poses both the piv ot ing and pric ing op era tions. The selfscheduling ap proach is both flexi ble and ef fi cient; its im ple men ta tion is close in speed to the best se rial code when us ing one proc es sor, and is ca pa ble of sub stan tial speed ups as par al lel com put ing units are added. An indepth com pu ta tional study of ran domly gen er ated trans por ta tion and trans ship ment prob lems veri fied the ef fec tive ness of this ap proach, with re sults on a 20processor 80386based sys tem that are com peti tive with—and oc ca sion ally su pe rior to—mas sively par al lel im ple men ta tions us ing tens of thou sands of proc es sors. A microanalysis of the code's be hav ior iden ti fied un ex pected sources of (the oc ca sion ally su per lin ear) speedup, in clud ing the evo lu tion ary to pol ogy of the net work ba sis.