Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares

Abstract

This paper discusses the problem of covering and hitting a set of line segments L in R2 by a pair of axis-parallel congruent squares of minimum size. We also discuss the restricted version of covering, where each line segment in L is to be covered completely by at least one square. The proposed algorithms assume that the input segments are given in a read-only array. For each of these problems (i.e. covering, hitting and restricted covering problems), our proposed algorithm reports the optimum result by executing only two passes of reading the input array sequentially. All these algorithms need only O(1) extra space. The solution of these problems also give a 2 approximation for covering and hitting those line segments L by two congruent disks of minimum radius with same computational complexity.