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We present an algorithm for linear programming which requires Ο(((m + n) n2 + (m + n)1.5 n) L) arithmetic operations where m is the number of inequalities, and n is the number of variables. Each operation is performed to a precision of Ο (L) bits. L is bounded by the number of bits in the input.
Pravin M. Vaidya (Thu,) studied this question.