Issue No. 02 - February (1987 vol. 36)
A.A. Bertossi , Department of Computer Science, University of Pisa
The use of a special-purpose VLSI chip for solving a linear programming problem is presented. The chip is structured as a mesh of trees and is designed to implement the well-known simplex algorithm. A high degree of parallelism is introduced in each pivot step, which can be carried out in O (log n) time using an m ? n mesh of trees having an O(mn log m log3 n) area where m - 1 and n - 1 are the number of constraints and variables, respectively. Two variants of the simplex algorithm are also considered: the two-phase method and the revised one. The proposed chip is intended as being a possible basic block for a VLSI operations research machine.
VLSI, Linear programming, mesh of trees, simplex algorithm, time complexity
A. Bertossi and M. Bonuccelli, "A VLSI Implementation of the Simplex Algorithm," in IEEE Transactions on Computers, vol. 36, no. , pp. 241-247, 1987.