Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
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It is shown that for any fixed number of variables, linear-programming problems with $n$ linear inequalities can be solved deterministically by $n$ parallel processors in sublogarithmic 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 take into account the operations needed for processor allocation, the time bound is $O((\log\log n)^{d+c})$, where $c$ is an absolute constant.