The k-Fréchet distance of polygonal curves

We introduce a new distance measure for comparing polygonal chains: the k-Fréchet distance. As the name implies it is closely related to the well-studied Fréchet distance but allows to find similarities between curves that resemble each other only piecewise. As we will explain it provides a nice transition between (weak) Fréchet distance and Hausdorff distance. We prove NPcompleteness for the k-Fréchet distance of polygonal curves in different variants and furthermore APX-completeness for the optimization version of our problem, discuss algorithmic approaches and present open questions.