Parallel Linear Programming in Fixed Dimension Almost Surely in Constant Time

For any xed dimension d, the linear programming problem with n inequality constraints can be solved on a probabilistic CRCW PRAM with O(n) processors almost surely in constant time. The algorithm always nds the correct solution. With nd= log2 d processors, the probability that the algorithm will not nish within O(d2 log2 d) time tends to zero exponentially with n.

• Type: Conference
• Year: 1990
• Where: FOCS
• Authors: Noga Alon, Nimrod Megiddo
• Keywords: FOCS 1990, Inequality Constraints, Linear Programming Problem, Probabilistic Crcw Pram, Theoretical Computer Science