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A deterministic poly(log log N)-time N-processor algorithm for linear programming in fixed dimension

1992
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Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92
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It is shown that for any x e d n umb e r o f v ariables, the linear programming problems with n linear inequalities can be solved deterministically by n parallel processors in sub-logarithmic time. The parallel time bound (counting only the arithmetic operations) is O((log log n) d ) where d is the number of variables. In the one-dimensional case this bound is optimal. If we t a k e i n to account the operations needed for processor allocation, the time bound is O((loglog n) d+c ) where c is an

doi:10.1145/129712.129744
dblp:conf/stoc/AjtaiM92
fatcat:spcyu4clq5gd3fpf4obmbhc6py