Tiling Rectangles with Rectangles
نویسندگان
چکیده
منابع مشابه
Tiling rectangles with holey polyominoes
We present a new type of polyominoes that can have transparent squares (holes). We show how these polyominoes can tile rectangles and we categorise them according to their tiling ability. We were able to categorise all but 7 polyominoes with 5 or fewer visible squares.
متن کاملTiling a Polygon with Rectangles
We study the problem of tiling a simple polygon of surface n with rectangles of given types (tiles). We present a linear time algorithm for deciding if a polygon can be tiled with 1 m and k 1 tiles (and giving a tiling when it exists), and a quadratic algorithm for the same problem when the tile types are m k and k m.
متن کاملTiling simply connected regions with rectangles
Abstract. In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two rectangles is NP-complete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can be solved in quadratic time (in the area). We prove that there is a finite set of at most 10 rectangles f...
متن کاملTiling by rectangles and alternating current
This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses directcurrent circuits. The new approach of the paper is an application of alternating-current circuits. The following results are obtained: • a necessary condition for a rectangle to be tilable by rectangles of given shapes; •...
متن کاملTiling a Polygon with Two Kinds of Rectangles
We fix two rectangles with integer dimensions. We give a quadratic time algorithm which, given a polygon F as input, produces a tiling of F with translated copies of our rectangles (or indicates that there is no tiling). Moreover, we prove that any pair of tilings can be linked by a sequence of local transformations of tilings, called flips. This study is based on the use of J. H. Conway’s tili...
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ژورنال
عنوان ژورنال: Mathematics Magazine
سال: 1982
ISSN: 0025-570X
DOI: 10.2307/2690096