In this paper, we consider 0/1 databases and provide an alternative way of extracting knowledge from such databases using tiles. A tile is a region in the database consisting solely of ones. The interestingness of a tile is measured by the number of ones it consists of, i.e., its area. We present an efficient method for extracting all tiles with area at least a given threshold. A collection of ...

The undecidable problems we saw at the start of our unit on undecidability were all questions about the behavior of computer programs. But in fact there are many decision problems which, on the surface, have nothing to do with computer programs yet can still be proved to have no algorithmic solution. One of these is a tiling problem. Imagine square tiles divided into colored triangular quadrants.

definition of packing and tiling.) Two recent papers by Freiling & Rinne 1994, and by Laczkovich & Szekeres 1995, turn the question around: For which sidelengths, s, can the square be packed by rectangles similar to 1 × s and s × 1? Employing a Dehn-functional and a theorem of Wall1945, they give this astonishing answer: Iff s is algebraic over , and all of its conjugates in the complex plane h...

Tiling is a well-known pattern mining technique. Traditionally, it discovers large areas of ones in binary databases or matrices, where an area is defined by a set of rows and a set of columns. In this paper, we introduce the novel problem of ranked tiling, which is concerned with finding interesting areas in ranked data. In this data, each transaction defines a complete ranking of the columns....

This paper describes an efficient method for constructing a tiling between a pair of planar contours. The problem is of interest in a number of domains, including medical imaging, biological research and geological reconstructions. Our method, based on ideas from multiresolution analysis and wavelets, requiresO(n) space and appears to require O(n logn) time for average inputs, compared to the O...

We consider a certain tiling problem of a planar region in which there are no long horizontal or vertical strips consisting of copies of the same tile. Intuitively speaking, we would like to create a dappled pattern with two or more kinds of tiles. We give an efficient algorithm to solve the problem, and discuss its applications in texturing.

We recently introduced a notion of tilings the geometric realization finite simplicial complex and related those to discrete Morse theory R. Forman, especially when they have property be shellable, shared by classical shellable complexes. now observe that every such tiling supports quiver which is acyclic precisely then shelling induces two spectral sequences converge (co)homology complex. Thei...

We consider questions concerning the tileability of orthogonal polygons with colored dominoes. A colored domino is a rotatable 2× 1 rectangle that is partitioned into two unit squares, which are called faces, each of which is assigned a color. In a colored domino tiling of an orthogonal polygon P , a set of dominoes completely covers P such that no dominoes overlap and so that adjacent faces ha...

Genomic tiling arrays are a type of DNA microarrays which can investigate the complete genome of arbitrary species for which the sequence is known. The design or selection of suitable oligonucleotide probes for such arrays is however computationally difficult if features such as oligonucleotide quality and repetitive regions are to be considered. We formulate the minimal cost tiling path proble...

To a given tiling a non commutative space and the corresponding C∗-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for discrete models of one or many particle systems on the tiling or its periodic identification. Its scaled ordered K0-group furnishes the gap labelling of Sch...