A deterministic poly(loglog n)-time n-processor algorithm for linear programming in fixed dimension

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((loglog 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((loglog n)d+c), where c is an absolute constant.