2 research outputs found
On optimal min-# curve simplification problem
In this paper we consider the classical min--\# curve simplification problem in three different variants. Let , be a polygonal curve with vertices in , and be a distance measure. We aim to simplify by another polygonal curve with minimum number of vertices satisfying . We obtain three main results for this problem: (1) An -time algorithm when is the Fr\'echet distance and vertices in are selected from a subsequence of vertices in . (2) An NP-hardness result for the case that is the directed Hausdorff distance from to and the vertices of can lie anywhere on while respecting the order of edges along . (3) For any , an -time algorithm that computes whose vertices can lie anywhere in the space and whose Fr\'echet distance to is at most with at most links, where is the number of links in the optimal simplified curve and hides polynomial factors of