Constructing the minimization diagram of a two-parameter problem

Authors:
David Fernández-Baca;S. Srinivasan
Affiliations:
Department of Computer Science, Iowa State University, Ames, IA 50011, USA;IBM Corporation, Rochester, MN 55901, USA
Venue:
Operations Research Letters
Year:
1991

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Abstract

Let P(@l @m) = min{@?"1(x)+@l@?"2(x)+@m@?"3(x)|x @e D}. We present a method that constructs P(@l, @m) for all @l, @m in a given interval in O(@?.T(n)+@?^2) time, where @? denotes the number of faces of P(@l, @m) in the interval and T(n) denotes the time needed to solve the associated nonparametric problem.