Investigating the sparse simplex algorithm on a distributed memory multiprocessor

There is a sustained interest in improving the computational performance of the sparse simplex (SSX) method for linear programs. Although there have b een some investigations covering SSX on parallel computing platforms the pe rformance results have not been particularly encouraging. While it is possi ble to analyze and understand the lack of success of SSX on parallel platfo rms we have found a set of benefits (alternative to performance enhancement only) that can be obtained by studying the behaviour of SSX on parallel pl atforms. In this paper we introduce a cooperating distributed processing al gorithm which is a novel implementation of the SSX. Our investigation of th is algorithm shows how the distributed parallel architecture is an ideal en vironment for studying the potentials of the serial SSX. Interestingly, it sheds new light on some ways the performance of SSX can be improved, We giv e account of our findings with some mixed pricing strategies. We point out, that our distributed algorithm also can serve as an extremely robustsolver that may be used to a great advantage in case of numerically difficult pro blems and for those problems for which there is no a priori knowledge of be st SSX strategies. (C) 2000 Elsevier Science B.V. All rights reserved.