Whilst Polyomino tiling theory has been extensively studied as a branch of research in mathematics, its application has been largely confined to multimedia, graphics and gaming domains. In this paper, we present a novel application of Tromino tiling theory, a class of Polyomino with three cells in the context of a reconfigurable floor cleaning robot, hTromo. The developed robot platform is able...

We compare two methods for entropy coding uniformly quantized wavelet coefficients: windowing, which uses local statistics to adapt the probability assignment and best tiling, which aims to compress as well as the best tiling of a subband with rectangular tiles of probability models. We find that on some synthetic images, the best tiling method works considerably better than windowing, but on a...

Several methods exploit the relative motion between the probe and the object being scanned to gure out an estimate of the normals of the existing structures in a volume. These methods are revealed as a good estimator for normals, at least better than simple gradient schemes. On the other hand, polygonal meshes can be obtained directly from raw data by means of tiling algorithms. Although these ...

We contribute to combinatorics and algorithmics of words by introducing new types of periodicities in words. A tiling period of a word w is partial word u such that w can be decomposed into several disjoint parallel copies of u, e.g. a b is a tiling period of aabb. We investigate properties of tiling periodicities and design an algorithm working in O(n log(n) log log(n)) time which finds a tili...

This paper examines a recomposition of the rhombic Penrose aperiodic protoset due to Robert Ammann. We show that the three prototiles that result from the recomposition form an aperiodic protoset in their own right without adjacency rules and that every tiling admitted by this protoset (here called an Ammann tiling) is mutually locally derivable with a Penrose tiling. Although these Ammann tili...

Good data locality is an important aspect of obtaining scalable performance for multigrid methods. However, locality can be difficult to achieve, especially when working with unstructured grids and sparse matrices whose structure is not known until runtime. Our previous work developed full sparse tiling, a runtime reordering and rescheduling technique for improving locality. We applied full spa...

1. Rep-tiling. This paper provides a short survey of recent work by the author on self-replicating tilings, a subject that has recently come under independent investigation by several mathematicians, for example Grr ochenig and Hass 11], Grr ochenig and Madyeh 10], Kenyon 14], Kitto, Vince and Wilson 15] and Vince 21] 22]. These tilings have application to computer addressing 5] 15] 20] and to ...

When can a given finite region consisting of cells in a regular lattice (triangular, square, or hexagonal) in [w’ be perfectly tiled by tiles drawn from a finite set of tile shapes? This paper gives necessary conditions for the existence of such tilings using boundary inuariants, which are combinatorial group-theoretic invariants associated to the boundaries of the tile shapes and the regions t...

For SOR-like PDE solvers, loop tiling either helps little in improving data locality or hurts their performance. This paper presents a novel compiler technique called code tiling for generating fast tiled codes for these solvers on uniprocessors with a memory hierarchy. Code tiling combines loop tiling with a new array layout transformation called data tiling in such a way that a significant am...