Abstract
Most algorithms of computational geometry are designed for the Real-RAM and non-degenerate input. We call such algorithms idealistic. Executing an idealistic algorithm with floating point arithmetic may fail. Controlled perturbation replaces an input x by a random nearby \(\tilde{x}\) in the δ-neighborhood of x and then runs the floating point version of the idealistic algorithm on \(\tilde{x}\). The hope is that this will produce the correct result for \(\tilde{x}\) with constant probability provided that δ is small and the precision L of the floating point system is large enough. We turn this hope into a theorem for a large class of geometric algorithms and describe a general methodology for deriving a relation between δ and L. We exemplify the usefulness of the methodology by examples.
Partially supported by the IST Programme of the EU under Contract No IST-006413, Algorithms for Complex Shapes (ACS).
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Mehlhorn, K., Osbild, R., Sagraloff, M. (2006). Reliable and Efficient Computational Geometry Via Controlled Perturbation. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_27
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DOI: https://doi.org/10.1007/11786986_27
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