Finding structures on imprecise points

Abstract

An imprecise point is a point in R^2 of which we do not know the location exactly; we only know for each point a region in R^2 containing it. On such a set of imprecise points, structures like the closest pair or convex hull are not uniquely defined. This leads us to study the following problem: Given a structure of interest, a set R of regions and a subset C ¿ R, we want to determine if it is possible to place a point in each region of R such that the points placed in regions of C form the structure of interest. We study this problem for the convex hull, with various types of regions. For each variant we either give a NP-hardness proof or a polynomial-time algorithm