Improved bounds for rectangular and guillotine partitions
نویسندگان
چکیده
منابع مشابه
Inproved Bounds for Rectangular and Guillotine Partitions
We study the problem of partitioning a rectangle S with a set of interior points Q into rectangles by introducing a set of line segments of least total length. The set of partitioning line segments must include every point in Q. Since this prob/em is computationally intractable (NP-hard), several approximation algorithms for its solution have been developed. In this paper we show that the lengt...
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We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula, and explicit formula. We find a connection between multidimensional permutations and guillotine partitions of a box. In particular, a bijection between separable d-dimensional permutations and guillotine partitions of a 2d−1-dimensional bo...
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Given a set of n points, P, in E d (the plane when d = 2) that lie inside a d-box (rectangle when d = 2) R, we study the problem of partitioning R into d-boxes by introducing a set of orthogonal hyperplane segments (line segments when d = 2) whose total (d?1)-volume (length when d = 2) is the least possible. In a valid d-box partition, each point in P must be included in at least one partitioni...
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A guillotine partition of a d-dimensional axis-aligned box B is a recursive partition of B by axis-aligned hyperplane cuts. The size of a guillotine partition is the number of boxes it contains. Two guillotine partitions are box-equivalent if their boxes satisfy compatible order relations with respect to the axes. (In many works, box-equivalent guillotine partitions are considered identical.) I...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1989
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(89)80042-2