Optimal Partitioning Which Maximizes the Weighted Sum of Products

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


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.


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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