๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Packing Rectangles with Congruent Polyominoes

โœ Scribed by William Rex Marshall


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
787 KB
Volume
77
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.

โœฆ Synopsis


Golomb has covered the main previous results of tiling a rectangle with congruent polyominoes in the revised edition of ``Polyominoes' ' (1994). This article attempts to summarise recent discoveries of many new examples of polyominoes which pack rectangles.


๐Ÿ“œ SIMILAR VOLUMES


Tiling Rectangles and Half Strips with C
โœ Michael Reid ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 322 KB

In the second edition of Golomb's classic ``Polyominoes'' [9], several infinite families of rectifiable polyominoes are given, but only nine sporadic examples are known. Curiously, two of these sporadic examples are related by a 2\_1 affine transformation (Fig. 1). This led us to consider the image

Tiling a Square with Eight Congruent Pol
โœ Michael Reid ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 76 KB

The problem of finding polyominoes that tile rectangles has attracted a lot of attention; see [1] for an overview, and [2, 3] for more recent results. Several general families of such polyominoes are known, but sporadic examples seem to be scarce. Marshall [2, Fig. 9] gives a polyomino of rectangula

Efficient Approximation Algorithms for T
โœ Piotr Berman; Bhaskar DasGupta; S Muthukrishnan; Suneeta Ramaswami ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 202 KB

We provide improved approximation algorithms for several rectangle tiling and packing problems (RTILE, DRTILE, and d-RPACK) studied in the literature. Most of our algorithms are highly efficient since their running times are near-linear in the sparse input size rather than in the domain size. In add