With the growth of internet usage, many kinds of useful data are served in the internet. Geographic data such as a map is one of them. However since geographic data is usually very huge, it needs special treatment in serving. One useful technique is tiling. For example, a map is divided into smaller pieces called a tile, and served tile by tile. Since the client usually requests several tiles i...

We present a method which splits an input image into a set of tiles. Each tile is then replaced by another image from a large database such that, when viewed from a distance, the original image is reproduced as well as possible. While the general concept of image mosaics is not new, we consider our results as "genuine image mosaics" (or short GIzMOs) in the sense that the images from the databa...

Multipartitioning is a strategy for decomposing multi-dimensional arrays into tiles and mapping the resulting tiles onto a collection of processors. This class of partitionings enables efficient parallelization of “line-sweep” computations that solve one-dimensional recurrences along each dimension of a multi-dimensional array. Multipartitionings yield balanced parallelism for line sweeps by as...

A classic problem in elementary combinatorics asks in how many ways one can tile a 1×n chessboard using 1× 1 and 1× 2 squares. The number of such tilings is the nth Fibonacci number. In a 2010 paper, Grimaldi generalized this problem by allowing for 1× 1 tiles to have one of w types and 1× 2 tiles to have one of t types and found that the solutions, in w and t, satisfied many of the same proper...

Abstract. This investigation studies the decidability problem of plane edge coloring with three symbols. In the edge coloring (or Wang tiles) of a plane, unit squares with colored edges that have one of p colors are arranged side by side such that the touching edges of the adjacent tiles have the same colors. Given a basic set B of Wang tiles, the decision problem is to find an algorithm to det...

We consider the problem of tiling a segment {0, . . . , n} of the discrete line. More precisely, we ought to characterize the structure of the patterns that tile a segment and their number. A pattern is a subset of N. A tiling pattern or tile for {0, . . . , n} is a subset A ∈ P(N) such that there exists B ∈ P(N) and such that the direct sum of A and B equals {0, . . . , n}. This problem is rel...

Virtual reality (VR) systems are used to create, display, and interact with virtual objects in space. They create an illusion of reality in 3-dimensions (3D) by providing a specific collection of technologies such as head mounted 3D displays, Glove input devices and audio systems. The goal of the research project was to develop a tangible and user-friendly 3D interface for spatial construction ...

In this paper we focus on algorithms and reconfigurable tiled architectures for streaming DSP applications. The tile concept has a number of advantages: (1) depending on the requirements more or less tiles can be switched on/off, (2) the tile structure fits well to future IC process technologies, more tiles will be available in advanced process technologies, but the complexity per tile stays th...