Square and Rectangle Covering with Outliers

Abstract

For a set of n points in the plane, we consider the axis-aligned (p; k)-Box COVERING problem: Find p axis-aligned, pairwise disjoint. boxes that together contain exactly n-k points. Here, our boxes are either squares or rectangles, and we want to minimize the area of the largest box. For squares, we present algorithms that find the solution in O(n + k log k) time for p = 1. and in O(n log n + k(p) log(p) k) time for p = 2; 3. For rectangles we have running times of O(n + k(3)) for p = 1 and O(n log n + k(2+p) log(p-1) k) time for p = 2; 3. In all cases; our algorithms use O(n) space.