Tiling a Rectangle with the Fewest 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.
متن کاملTiling a Rectangle with Polyominoes
A polycube in dimension d is a finite union of unit d-cubes whose vertices are on knots of the lattice Zd . We show that, for each family of polycubes E, there exists a finite set F of bricks (parallelepiped rectangles) such that the bricks which can be tiled by E are exactly the bricks which can be tiled by F . Consequently, if we know the set F , then we have an algorithm to decide in polynom...
متن کاملA special tiling of the rectangle
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.
متن کاملA 28-Approximation Algorithm for Rectangle Tiling
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...
متن کاملTiling with L’s and Squares
We consider tilings of 2 × n, 3 × n, and 4 × n boards with 1 × 1 squares and Lshaped tiles covering an area of three square units, which can be used in four different orientations. For the 2 × n board, the recurrence relation for the number of tilings is of order three and, unlike most third order recurrence relations, can be solved exactly. For the 3 × n and 4 × n board, we develop an algorith...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1996
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0104