Iwano, Misono, Tezuka, and Fujishige (1990) have given an approximate binary search algorithm for computing max mean cuts. This paper gives a short proof of the correctness of their algorithm. It also shows how their ...
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Iwano, Misono, Tezuka, and Fujishige (1990) have given an approximate binary search algorithm for computing max mean cuts. This paper gives a short proof of the correctness of their algorithm. It also shows how their algorithm can be dualized to an approximate binary search algorithm for computing min mean cycles that is as fast as but simpler than Orlin and Ahuja's algorithm (1992).
A fast approximation algorithm for the multiple-choice knapsack problem is proposed whose solution is guaranteed to be 4/5-bounded. The algorithm is based on binarysearch and runs in O(n log m) time, n being the tota...
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A fast approximation algorithm for the multiple-choice knapsack problem is proposed whose solution is guaranteed to be 4/5-bounded. The algorithm is based on binarysearch and runs in O(n log m) time, n being the total number of items and m the number of multiple-choice classes in the knapsack problem. (C) 1998 Elsevier Science B.V. All rights reserved.
We study succinct representations of a convex univariate function phi over a finite domain. We show how to construct a succinct representation, namely a piecewise-linear function (phi) over bar approximating phi when ...
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We study succinct representations of a convex univariate function phi over a finite domain. We show how to construct a succinct representation, namely a piecewise-linear function (phi) over bar approximating phi when given a black box access to an L-approximation oracle (phi) over tilde of phi (the oracle value is always within a multiplicative factor L from the true value). The piecewise linear function (phi) over bar has few breakpoints (poly-logarithmic in the size of the domain and the function values) and approximates the true function phi up to a (1+epsilon)L-2 multiplicative factor point-wise, for any epsilon > 0. This function (phi) over bar is also convex so it can be used as a replacement for the original function and be plugged in algorithms in a black box fashion. Finally, we give positive and negative results for multivariate convex functions. (C) 2014 Elsevier B.V. All rights reserved.
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