Abstract
Finding the similarity between curves is an important problem that comes up in many areas such as 3D modeling, GIS applications, ordering, and reachability. A related problem is to find one of the curves given a measure of similarity and another curve. Given a set of points S, a polygonal curve P, and an ε>0, the discrete set-chain matching problem is to find another polygonal curve Q such that the nodes of Q are points in S and dF(P,Q)≤ε. Here, dF is the discrete Fréchet distance between the two polygonal curves. For the first time we study the set-chain matching problem based on the discrete Fréchet distance rather than the continuous Fréchet distance. We further extend the problem based on unique or non-unique nodes and on limiting the number of points used. We prove that three of the variations of the set-chain matching problem are NP-complete. For the version of the problem that is polynomial, we give an O(|P||S|) time greedy solution.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
