, Volume 47, Issue 1-3, pp 175-201

An algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations

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Abstract

We present an algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations wherem is the number of constraints, andn is the number of variables. Each operation is performed to a precision of O(L) bits.L is bounded by the number of bits in the input. The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of \(\sqrt {m + n} \) .