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Optimization in arrangements

par Langerman, Stefan ;Steiger, William W.
Référence Lecture notes in computer science, 2607, page (50-61)
Publication Publié, 2003

Article révisé par les pairs

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Résumé :

Many problems can be formulated as the optimization of functions in R 2 which are implicitly defined by an arrangement of lines, halfplanes, or points, for example linear programming in the plane. We present an efficient general approach to find the optimum exactly, for a wide range of functions that possess certain useful properties. To illustrate the value of this approach, we give a variety of applications in which we speed up or simplify the best known algorithms. These include algorithms for finding robust geometric medians (such as the Tukey Median), robust regression lines, and ham-sandwich cuts. © Springer-Verlag Berlin Heidelberg 2003.