Abstract
Given a set ofn iso-oriented rectangles in the plane whose sides are parallel to the coordinate axes, we consider the rectangle intersection problem, i.e., finding alls intersecting pairs. The problem is well solved in the past and its solution relies heavily on unconventional data structures such as range trees, segment trees or rectangle trees. In this paper we demonstrate that classical divide-and-conquer technique and conventional data structures such as linked lists are sufficient to achieve a time bound ofO(n logn) +s, and a space bound of Θ(n), both of which are optimal.
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Supported in part by the National Science Foundation under Grants MCS 8342682 and ECS 8340031.
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Lee, D.T. An optimal time and minimal space algorithm for rectangle intersection problems. International Journal of Computer and Information Sciences 13, 23–32 (1984). https://doi.org/10.1007/BF00989481
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DOI: https://doi.org/10.1007/BF00989481