Modern computational geometry plays a critical role across a vast number of diverse
research fields where theoretical results for provably efficient algorithms are necessary …

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 …

We define and study the Fréchet distance and the discrete Fréchet distance between two
point sets in the plane. One problem based on the well-known Fréchet distance is to find a …

In the first part of this thesis, we consider an instance of Frechet distance problem in which
the speed of traversal along each segment of the curves is restricted to be within a specfied …

We revisit the problem of deciding whether a given curve resembles some part of a larger
curve under a fixed Fréchet distance, achieving a running time of O (nm), for n and m being …

In this paper we focus on the map matching problem where the goal is to find a path through
a planar graph such that the path through the vertices closely matches a given polygonal …

Finding the similarity between paths is an important problem that comes up in many areas
such as 3D modeling, GIS applications, ordering, and reachability. Given a set of points S, a …

Let P be a polygonal curve in R^ d of length n, and S be a point-set of size k. We consider
the problem of finding a polygonal curve Q on S such that all points in S are visited and the …

We study the problem of computing the upper bound of the discrete Fr\'{e} chet distance for
imprecise input, and prove that the problem is NP-hard. This solves an open problem posed …

Recent research on interactive electronic systems, like computers, can improve the quality of
life of many researchers, students, professors, etc. In the case of disabled people …