Computing constrained minimum-width annuli of point sets

Computing Constrained Minimum-Width Annuli of Point Sets

Constrained Minimum - WidthAnnuli of Point Sets ?

We study the problem of determining whether a manufactured disc of certain radius r is within tolerance. More precisely, we present algorithms that, given a set of n probe points on the surface of the manufactured object, compute the thinnest annulus whose outer (or inner, or median) radius is r and that contains all the probe points. Our algorithms run in O(n log n) time.

Approximation Algorithms for Minimum-Width Annuli and Shells

Computing Minimum Diameter Color-Spanning Sets

We study the minimum diameter color-spanning set problem which has recently drawn some attention in the database community. We show that the problem can be solved in polynomial time for L1 and L∞ metrics, while it is NP-hard for all other Lp metrics even in two dimensions. However, we can efficiently compute a constant factor approximation.

Computing the Center of Planar Point Sets

Given a collection H of n lines in the plane, the level of a point x is the number of lines of H lying below x or passing thru x. We show that for a given k, one can compute the convex hull of the set of points of level k, in time O(n log 4 n). This implies that a description of the set of centerpoints of a given n-point set in the plane can be found within the same time bound, and a point of g...