Covering a square by small perimeter rectangles
نویسندگان
چکیده
منابع مشابه
Covering a Square by Small Perimeter Rectangles
We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2m + 1)/(n + m(m + 1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m + 1) (or m2).
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Alon, N. and D.J. Kleitman, Partitioning a rectangle into small perimeter rectangles, Discrete Mathematics 103 (1992) 111-119. We show that the way to partition a unit square into kZ + s rectangles, for s = 1 or s = -1, so as to minimize the largest perimeter of the rectangles, is to have k 1 rows of k identical rectangles and one row of k + s identical rectangles, with all rectangles having th...
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The problem of covering a compact canonical polygonal region, called target region, with a finite family of rectangles is considered. Tools for mathematical modeling of the problem are provided. Especially, a function, called Γ-function, is introduced which indicates whether the rectangles with respect to their configuration form a cover of the target region or not. The construction of the Γ-fu...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1986
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02187679