Approximating SVPinfty to within Almost-Polynomial Factors Is NP-Hard
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
On simultaneous approximation in quadratic integer programming
Operations Research Letters
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We present a preprocessing algorithm to make certain polynomial algorithms strongly polynomial. The running time of some of the known combinatorial optimization algorithms depends on the size of the objective function w. Our preprocessing algorithm replaces w by an integral valued w whose size is polynomially bounded in the size of the combinatorial structure and which yields the same set of optimal solutions as w. As applications we show how existing polynomial algorithms for finding the maximum weight clique in a perfect graph and for the minimum cost submodular flow problem can be made strongly polynomial. The method relies on Lovász's simultaneous approximation algorithm.