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Optimal Partitioning Which Maximizes the Weighted Sum of Products

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)

Abstract

We consider the problem of partitioning n real numbers to K nonempty groups, so that the weighted sum of products over all groups is maximized. Formally, given \(S=\{r_1,\ldots ,r_n\}\) and \(W=(w_1,\ldots ,w_K)\) where \(w_i\ge 0\), we look for a partition of S into K nonempty groups \(S_1,\ldots ,S_K\), so that \(\sum _{g=1}^{K} (w_g\cdot \prod _{r_j\in S_g}r_j)\) is maximized. Our main result is an \(O(n^2)\) time algorithm for finding an optimal partition.

Keywords

Partitioning with additive objective K-partition Sum of products Greedy algorithms Rearrangement inequality 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Hong KongPokfulamHong Kong SAR, China

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