Parallel linear programming in fixed dimension almost surely in constant time

For any fixed dimension <?Pub Fmt italic>d<?Pub Fmt /italic>, thelinear programming problem with <?Pub Fmt italic>n<?Pub Fmt /italic>inequality constraints can be solved on a probabilistic CRCW PRAM with<?Pub Fmt italic>O<?Pub Fmt /italic>(<?Pub Fmt italic>n<?Pub Fmt /italic>)processors almost surely in constant time. The algorithm always findsthe correct solution. With<?Pub Fmt italic>nd<?Pub Fmt /italic>/log<supscrpt>2</supscrpt><?Pub Fmt italic>d<?Pub Fmt /italic>processors, the probability that the algorithm will not finish within<?Pub Fmt italic>O<?Pub Fmt /italic>(<?Pub Fmt italic>d<?Pub Fmt /italic><supscrpt>2</supscrpt>log<supscrpt>2</supscrpt><?Pub Fmt italic>d<?Pub Fmt /italic>time tends to zero exponentially with<?Pub Fmt italic>n<?Pub Fmt /italic>. <abstrbyl>—<?Pub Fmt italic><?Pub Caret>Authors' Abstract<?Pub Fmt /italic></abstrbyl>