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2006

One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

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One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions
Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned ni numbers with ni lying in a given range. The goal is to maximize a Schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n1, . . . , np) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a maj...
F. H. Chang, H. B. Chen, J. Y. Guo, Frank K. Hwang
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JCO
Authors F. H. Chang, H. B. Chen, J. Y. Guo, Frank K. Hwang, Uriel G. Rothblum
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