Computing the Fréchet distance between uncertain curves in one dimension

We consider the problem of computing Fréchet distance between two curves for which exact locations vertices are unknown. Each vertex may be placed in a given uncertainty region that vertex, and objective is to place so as minimise distance. This was recently shown NP-hard 2D, it unclear how compute an optimal placement at all. present first general algorithmic framework this problem. prove results polynomial-time algorithm 1D with intervals regions. In contrast, we show case maximise also study weak uncertain curves. While finding seems more difficult than regular distance—and indeed can easily 2D—the computed polynomial time. Finally, investigate discrete distance, which, somewhat surprisingly, already 1D.