Abstract. Point constellation recognition is a common problem with many pattern matching applications. Whilst useful in many contexts, this work is mainly motivated by fingerprint matching. Fingerprints are traditionally modelled as constellations of oriented points called minutiae. The fingerprint verifier's task consists in comparing two point constellations. The compared constellations may differ by rotation and translation or by much more involved transforms such as distortion or occlusion. This paper presents three new constellation matching algorithms. The first two methods generalize an algorithm by Bringer and Despiegel. Our third proposal creates a very interesting analogy between mechanical system simulation and the constellation recognition problem.

It is known that the longest simple path in the divisor graph that uses integers ≤ N is of length ≍ N/ log N . We study the partitions of {1, 2, . . . , N } into a minimal number of paths of the divisor graph, and we show that in such a partition, the longest path can have length asymptotically N 1−o(1) .

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