Space Efficient Approximation of Piecewise Linear Functions

In this work, we compute upper bounds of piecewise linear functions which is a special case of piecewise linear approximation. There are several application areas like pattern recognition or cartography. The goal is to reduce the number of sampling points while still preserving the characteristics of given data. The problem of approximating a given piecewise linear function with n sampling points by another piecewise linear function such that the euclidean distance between the two functions is limited by an error bound and the number of the resultant sampling points is minimum can be solved in O(n) time. Therefore, we study and implement an algorithm of Imai and Iri [II87]. We describe the basic idea and all needed components in detail. In our experiments we examine the results and analyse the benefit for our application, time-dependent route planning.