The decomposition of a square into rectangles of minimal perimeter. (English) Zbl 0603.05012
This paper solves the problem of subdividing a unit square into p rectangles of area 1/p in such a way that the maximal perimeter of a rectangle is as small as possible. The correctness of the solution is proved using the well-known theorems of Menger and Dilworth.
MSC:
| 05B45 | Combinatorial aspects of tessellation and tiling problems |
References:
| [1] | Kasif, S.; Klette, R., A data allocation problem for SIMD computers, Center for Automation Research, University of Maryland, Tech. Rept. CAR-TR-11 (1983) |
| [2] | Alon, N.; Kleitman, D. J., Covering a square by small perimeter rectangles, Discrete and Computational Geometry, 1, 1-7 (1986) · Zbl 0601.52009 |
| [3] | Bollobás, B., Graph Theory: An Introductory Course, (Graduate Texts in Math, 63 (1979), Springer: Springer New York) · Zbl 0688.05016 |
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