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This paper discusses the problem of covering and hitting a set of linesegments $\cal L$ in ${\mathbb R}^2$ by a pair of axis-parallel squares suchthat the side length of the larger of the two squares is minimized. We alsodiscuss the restricted version of covering, where each line segment in $\cal L$is to be covered completely by at least one square. The proposed algorithm forthe covering problem reports the optimum result by executing only two passes ofreading the input data sequentially. The algorithm proposed for the hitting andrestricted covering problems produces optimum result in $O(n)$ time. All theproposed algorithms are in-place, and they use only $O(1)$ extra space. Thesolution of these problems also give a $\sqrt{2}$ approximation for coveringand hitting those line segments $\cal L$ by two congruent disks of minimumradius with same computational complexity.

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