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Linear Algorithms in Sublinear Time—a Tutorial on Statistical Estimation
March/April 2011 (vol. 31 no. 2)
pp. 58-66
Torsten Ullrich, Fraunhofer Austria Research
Dieter W. Fellner, Fraunhofer IGD
This tutorial presents probability theory techniques for boosting linear algorithms. The approach is based on statistics and uses educated guesses instead of comprehensive calculations. Because estimates can be calculated in sublinear time, many algorithms can benefit from statistical estimation. Several examples show how to significantly boost linear algorithms without negative effects on their results. These examples involve a Ransac algorithm, an image-processing algorithm, and a geometrical reconstruction. The approach exploits that, in many cases, the amount of information in a dataset increases asymptotically sublinearly if its size or sampling density increases. Conversely, an algorithm with expected sublinear running time can extract the most information.

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Index Terms:
computations on discrete structures, geometrical problems and computations, statistical computing, computer graphics, graphics and multimedia
Torsten Ullrich, Dieter W. Fellner, "Linear Algorithms in Sublinear Time—a Tutorial on Statistical Estimation," IEEE Computer Graphics and Applications, vol. 31, no. 2, pp. 58-66, March-April 2011, doi:10.1109/MCG.2010.21
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