Improved Algorithms for Partial Curve Matching

Back in 1995, Alt and Godau gave an efficient algorithm for deciding whether a given curve resembles some part of a larger curve under a fixed Fr´echet distance, achieving a running time of O(nm log(nm)), for n and m being the number of segments in the two curves, respectively. We improve this long-standing result by presenting an algorithm that solves this decision problem in O(nm) time. Our solution is based on constructing a simple data structure which we call free-space map. Using this data structure, we obtain improved algorithms for several variants of the Fr´echet distance problem, including the Fr´echet distance between two closed curves, and the so-called minimum/maximum walk problems. We also improve the map matching algorithm of Alt et al. for the case when the map is a directed acyclic graph.

• Type: Journal
• Year: 2011
• Where: ESA
• Authors: Anil Maheshwari, Jörg-Rüdiger Sack, Kaveh Shahbaz, Hamid Zarrabi-Zadeh
• Keywords: Acyclic Graph, Algorithms, Data Structure, Decision Problem, ESA 2011