Parallel linear programming in fixed dimension almost surely in constant time

Authors:
N. Alon;N. Megiddo
Affiliations:
IBM Almaden Res. Center, San Jose, CA, USA;-
Venue:
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Year:
1990

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Abstract

It is shown that, for any fixed dimension d, the linear programming problem with n inequality constraints can be solvent on a probabilistic CRCW PRAM (concurrent-read-concurrent-write parallel random-access machine) with O(n) processors almost surely in constant time. The algorithm always finds the correct solution. With nd/log/sup 2/d processors, the probability that the algorithm will not finish within O(d/sup 2/log/sup 2/d) time tends to zero exponentially with n.