Minimum tiling of a rectangle by squares
نویسندگان
چکیده
منابع مشابه
Tiling a Rectangle with the Fewest Squares
We show that a square-tiling of a p × q rectangle, where p and q are relatively prime integers, has at least log2 p squares. If q > p we construct a square-tiling with less than q/p+C log p squares of integer size, for some universal constant C.
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We count tilings of a rectangle of integer sides m − 1 and n − 1 by a special set of tiles. The result is obtained from the study of the kernel of the adjacency matrix of an m × n rectangular subgraph in Z × Z.
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We study the following problem. Given ann×n arrayA of nonnegative numbers and a natural number p, partition it into at most p rectangular tiles, so that the maximal weight of a tile is minimized. A tile is any rectangular subarray of A. The weight of a tile is the sum of the elements that fall within it. In the partition the tiles must not overlap and are to cover the whole array. We give a 2 8...
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The problem that we consider is the following: given an n × n array A of positive numbers, find a tiling using at most p rectangles (which means that each array element must be covered by some rectangle and no two rectangles must overlap) that minimizes the maximum weight of any rectangle (the weight of a rectangle is the sum of elements which are covered by it). We prove that it is NP-hard to ...
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ژورنال
عنوان ژورنال: Annals of Operations Research
سال: 2018
ISSN: 0254-5330,1572-9338
DOI: 10.1007/s10479-017-2746-2