On the Exact Size of the Binary Space Partitioning of Sets of Isothetic Rectangles with Applications
نویسندگان
چکیده
We show an upper bound of 3n on size of the Binary Space Partitioning (BSP) tree for a set of n isothetic rectangles, and an upper bound of 2n if the rectangles tile the underlying space. This improves the bound of 12n from [PY92] and 4n in [NW95, dAF92]. The BSP tree is one of the most popular data structures and even “small” factor improvements of 4/3 or 2 we show improves the performance of applications relying on the BSP tree. Furthermore, our upper bounds yield improved approximation algorithms for several rectangular tiling problems in the literature. We also a show a lower bound of 2n in the worst case for a BSP for n isothetic rectangles, and a lower bound of 1.5n if they must form a tiling of the space.
منابع مشابه
Exact Size of Binary Space Partitionings and Improved Rectangle Tiling Algorithms
We prove the following upper and lower bounds on the exact size of binary space partition (BSP) trees for a set of n isothetic rectangles in the plane: • An upper bound of 3n− 1 in general, and an upper bound of 2n− 1 if the rectangles tile the underlying space. This improves the upper bounds of 4n in [V. Hai Nguyen and P. Widmayer, Binary Space Partitions for Sets of Hyperrectangles, Lecture N...
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