Summary: Where to build a temple, and where to dig to find one
Greg Aloupis
Jean Cardinal
S´ebastien Collette
John Iacono§
Stefan Langerman¶
Abstract
In this paper, we analyze the time complexity of find-
ing regular polygons in a set of n points. We use two
different approaches to find regular polygons, depend-
ing on their number of edges. Those with o(n0.068
)
edges are found by sweeping a line through the set of
points, while the larger polygons are found by ran-
dom sampling. We can find all the polygons with
high probability in O(n2.068+
) expected time for ev-
ery positive . This compares well to the O(n2.136+
)
deterministic algorithm of Brass [1]. Our method

Source: Aloupis, Greg - Département d'Informatique, Université Libre de Bruxelles
Collette. Sébastien - Département d'Informatique, Université Libre de Bruxelles

Collections: Computer Technologies and Information Sciences; Mathematics