# The Vector Partition Problem for Convex Objective Functions

@article{Onn2001TheVP,
title={The Vector Partition Problem for Convex Objective Functions},
author={Shmuel Onn and Leonard J. Schulman},
journal={Math. Oper. Res.},
year={2001},
volume={26},
pages={583-590}
}
• Published 1 August 2001
• Mathematics, Computer Science
• Math. Oper. Res.
Thepartition problem concerns the partitioning of a given set ofn vectors ind-space intop parts to maximize an objective function that is convex on the sum of vectors in each part. The problem has broad expressive power and captures NP-hard problems even if eitherp ord is fixed. In this article we show that when bothp,d are fixed, the problem is solvable in strongly polynomial time usingO(n d(p-1)-1) arithmetic operations. This improves upon the previously known bound ofO( ndp 2 ). Our method…
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