# An Algorithm for Canonical Forms of Finite Subsets of $$\mathbb {Z}^d$$Zd up to Affinities

@article{Paolini2017AnAF, title={An Algorithm for Canonical Forms of Finite Subsets of \$\$\mathbb \{Z\}^d\$\$Zd up to Affinities}, author={Giovanni Paolini}, journal={Discrete & Computational Geometry}, year={2017}, volume={58}, pages={293-312} }

In this paper we describe an algorithm for the computation of canonical forms of finite subsets of $$\mathbb {Z}^d$$Zd, up to affinities over $$\mathbb {Z}$$Z. For fixed dimension d, this algorithm has worst-case asymptotic complexity $$O(n \log ^2 n \, s\,\mu (s))$$O(nlog2nsμ(s)), where n is the number of points in the given subset, s is an upper bound to the size of the binary representation of any of the n points, and $$\mu (s)$$μ(s) is an upper bound to the number of operations required to… CONTINUE READING

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