We present an algorithm for compressing pattern databases (PDBs) and a method for fast random access of these compressed PDBs. We demonstrate the effectiveness of our technique by compressing two 6-tile sliding-tile PDBs by a factor of 12 and a 7-tile sliding-tile PDB by a factor of 24.

Centuries ago, European builders developed a reliable means of installing tile for high-traffic, high-use applications which relied on the laying of a sand strata between the structural substrate and the mortar-bed/tile composite top layer. Due to space (height) requirements and other concerns, the sand strata method for tile installation is, for all practical purposes, extinct. Modern theory, ...

We present a method for generating well-distributed point according to a given density. Our method is based on a single precomputed tile. The tile is both self-similar and hierarchical. A selfsimilar tile allows to increase the density of points in large steps by recursively subdividing the tile. A hierarchical tile allows to smoothly adjust the density of points. We present an interesting meth...

Tile-based self-assembly is a model of “algorithmic crystal growth” in which square “tiles” represent molecules that bind to each other via specific and variable-strength bonds on their four sides, driven by random mixing in solution but constrained by the local binding rules of the tile bonds. In the late 1990s, Erik Winfree introduced a discrete mathematical model of DNA tile assembly called ...

OIl August 4, 1906, I resected tile left tibial diaphysis of a girl aged fourteen years for sarcoma diagnosed clinically and radiologically (Figs. I and 2). Tile segment excised was replaced by a graft of equal length from tile fibula, the soft tissue attacilments of which were disturbed as little as possible durillg mobilisation in order to preserve tile blood supply. My reason for undertaking...