@inbook{23e5fdae9f764f15a6406821bfd97e61,
title = "Optimization in arrangements",
abstract = "Many problems can be formulated as the optimization of functions in R2 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.",
author = "Stefan Langerman and William Steiger",
year = "2003",
doi = "10.1007/3-540-36494-3_6",
language = "American English",
isbn = "3540006230",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "50--61",
editor = "Helmut Alt and Michel Habib",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "Germany",
}