Maxmin Location of an Anchored Ray in 3-Space and Related Problems (Extended Abstract)

We consider the problem of locating a ray emanating from the origin of 3-space such as to maximize the minimum weighted Euclidean distance to a set of weighted obstacles (points, lines or line segments). We present algorithms based on the parametric search paradigm which run in O(n log 4 n) time in the case of point obstacles, and in O(n 2 log 2 n) (O(n 2 log 2 n 2 ff(n) )) time in the case of line (segment) obstacles. We also show that for practically interesting restricted settings of the line obstacle problem, subquadratic algorithms can be obtained. Furthermore we discuss some related problems