Congruence Testing in High Dimensions

by · Jul 23, 2016 · 356 views ·

I will survey algorithms for testing whether two point sets are congruent, that is, equal up to a 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. I will then discuss algorithms for higher dimensions, and in particular, highlight the unpublished contributions of Jiří Matoušek. Finally, I will sketch our recent algorithm for four dimensions with near-linear running time (joint work with Heuna Kim).

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