Matevž Pavlič (2012) Computing triangulation of points in the plane using the GPU. EngD thesis.
The thesis deals with the problem of triangulation in a real plane using a graphics processing unit, specifically the CUDA architecture. An additional requirement posed is that the calculated triangulation should have the least possible total edge length. The problem thus defined is of the NP complexity. There are a number of different methods for reaching the desired solution, but we do not know which of these are appropriate for running on a graphics processing unit. In this paper we consider three methods. For two of these we have developed a sequential and a parallel algorithm; the latter is intended for running on the graphics processing unit. A series of tests were also carried out, with the purpose of optimising and comparing the efficiency of the parallel algorithms. The parallel algorithm was faster only with one of the methods. As this method is least efficient on sequential computer, the time this algorithm requires for execution is still longer than the execution time of the sequential algorithm with the other method. We did not manage to find a fast enough parallel algorithm for the other two methods. This is because they are of the recursive type and cannot be implemented in a way that would give a small number of branchings, this being the main condition necessary for an efficient execution of a parallel algorithm on a graphics unit processor. The study did not produce more efficient algorithms, but this negative result – i. e. the finding that it is very difficult to make efficient sequential methods parallel – is in itself interesting and can serve as a starting point for further work in this area.
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