@inproceedings{e8e1b276c5a04c028b5a528b5a6a13b8,

title = "Computing a center-transversal line",

abstract = "A center-transversal line for two finite point sets in R3 is a line with the property that any closed halfspace that contains it also contains at least one third of each point set. It is known that a center-transversal line always exists [12,24], but the best known algorithm for finding such a line takes roughly n12 time. We propose an algorithm that finds a center-transversal line in O(n1+εκ2(n)) worst-case time, for any ε>0, where κ(n) is the maximum complexity of a single level in an arrangement of n planes in R3. With the current best upper bound κ(n) = O(n5/2) of [21], the running time is O(n6+ε), for any ε>0. We also extend the concept of center-transversal line to that of bichromatic depth of lines in space, and give an algorithm that computes a deepest line exactly in time O(n1+εκ2(n)), and a linear-time approximation algorithm that computes, for any specified δ>0, a line whose depth is at least 1 − δ times the maximum depth.",

author = "Agarwal, {Pankaj K.} and Sergio Cabello and Sellar{\`e}s, {J. Antoni} and Micha Sharir",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2006.; 26th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2006 ; Conference date: 13-12-2006 Through 15-12-2006",

year = "2006",

doi = "10.1007/11944836_11",

language = "אנגלית",

isbn = "9783540499947",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "93--104",

editor = "Arun-Kumar, {[initials] N.}",

booktitle = "FSTTCS 2006",

}