On Finding the Maximum and Minimum Density Axes-parallel Regions in IRd

Abstract

Finding the density of a set of n points, especially where points are in IR 2 or IR 3 , has direct applications in thermal analysis of VLSI chips. In this paper, we consider identifying the maximum-density axes-parallel region for a set of weighted points in IR d for d ≥ 2, and show that it can be done in O(dn 2 ) time. We also consider finding the minimum-density axes-parallel region, and show that for IR 2 the problem can be solved in O(n 2 ) time.