2012/05/07 by Dan Chen, Pat Morin, Chen, Dan +1
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #cs.CG
paper · pdf · doi:10.48550/arxiv.1205.1524
9 pages; no figures
arxiv created 2013/06/14 · arxiv updated 2013/06/17
We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a Monte-Carlo data structure for this problem that can be constructed in O(nlog n) time, can answer queries O((log n)4/3) expected time, and answers correctly with high probability.