Abstract
I will survey algorithms for testing whether two point sets are congruent, that is, equal up to an Euclidean isometry. I will introduce the important techniques for congruence testing, namely dimension reduction and pruning, or more generally, condensation. I will illustrate these techniques on the three-dimensional version of the problem, and indicate how they lead for the first time to an algorithm for four dimensions with near-linear running time (joint work with Heuna Kim). On the way, we will encounter some beautiful and symmetric mathematical structures, like the regular polytopes, and Hopf-fibrations of the three-dimensional sphere in four dimensions.
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Rote, G. (2016). Congruence Testing of Point Sets in Three and Four Dimensions. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_4
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