ROBUST NONPARAMETRIC SIMPLIFICATION OF POLYGONAL CHAINS∗ STEPHANE DUROCHER, ALEXANDRE LEBLANC, JASON MORRISON and MATTHEW SKALA

In this paper we present a novel nonparametric method for simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. Specifically, given a sequence P of n points in the plane that determine a simple polygonal chain consisting of n− 1 segments, we describe algorithms for selecting a subsequence Q ⊂ P (including the first and last points of P ) that determines a second polygonal chain to approximate P , such that the number of crossings between the two polygonal chains is maximized, and the cardinality of Q is minimized among all such maximizing subsets of P . Our algorithms have respective running times O(n2 logn) (respectively, O(n2 √ logn)) when P is monotonic and O(n2 log n) (respectively, O(n2 log n)) when P is any simple polygonal chain in the Real RAM model (respectively, in the Word RAM model).