Improved algorithms for partial curve matching

Authors:
Anil Maheshwari;Jörg-Rüdiger Sack;Kaveh Shahbaz;Hamid Zarrabi-Zadeh
Affiliations:
School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
Venue:
ESA'11 Proceedings of the 19th European conference on Algorithms
Year:
2011

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Abstract

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 Fréchet distance, achieving a running time of O(nmlog(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 Fréchet distance problem, including the Fréchet 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.