In this paper we face the problem of computing a conservative approximation of a set of isothetic rectangles in the plane by means of a pair of enclosing isothetic rectangles. We propose an $O(n\log n)$ time algorithm for finding, given a set $M$ of $n$ isothetic rectangles, a pair of isothetic rectangles $(s,t)$ such that $s$ and $t$ enclose all rectangles of $M$ and {\em area\/}$(s) +$ {\em area\/}$(t)$ is minimal. Moreover we prove an $O(n\log n)$ lower bound for the one-dimensional version of the problem.
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