We consider the problem of reporting the pairwise enclosures in a set of n axesparallel rectangles in IR 2 , which is equivalent to reporting dominance pairs in a set of n points in IR 4 . O v er a decade ago, Lee and Preparata 6 gave a n O(n log 2 n + k){time and O(n){space algorithm for these problems, where k is the number of reported pairs. Since that time, the question of whether there is a faster algorithm has remained an intriguing open problem. In this paper, we give an algorithm which

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... s e s O(n) space and runs in O(n log n log log n+ k log log n) time. Thus, although our result is not a strict improvement o ver the Lee{ Preparata algorithm for the full range of k, it is, nevertheless, the rst result since Ref. (6) to make any progress on this long{standing open problem. Our algorithm is based on the divide{and{conquer paradigm. The heart of the algorithm is the solution to a red{blue dominance reporting problem (the \merge" step). We give a n o vel solution for this problem which is based on the iterative application of a sequence of non{trivial sweep routines. This solution technique should be of independent i n terest. We also present another algorithm whose bounds match the bounds given in Ref. (6) , but which is simpler. Finally, w e consider the special case where the rectangles have a small number, , of di erent aspect ratios, which is often the case in practice. For this problem, we give an algorithm which r u n s i n O( n logn + k) time and uses O(n) space.