COVERING A SET OF POINTS IN MULTIDIMENSIONAL SPACE

Let P = {p1, p2,...,p(n)} be a set of points in d-space. We study the problem of covering with the minimum number of fixed-size orthogonal hypersquares (CS(d) for short) all points in P. We present a fast approximation algorithm that generates provably good solutions and an improved polynomial-time approximation scheme for this problem. A variation of the CS(d) problem is the CR(d) problem, covering by fixed-size orthogonal hyperrectangles, where the covering of the points is by hyperrectangles with dimensions D1, D2,...,D(d) instead of hypersquares of size D. Another variation is the CD(d) problem, where we cover the set of points with hyperdiscs of diameter D. Our algorithms can be easily adapted to these problems.