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Approximating the Integral Fréchet Distance

Authors Anil Maheshwari, Jörg-Rüdiger Sack, Christian Scheffer



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Anil Maheshwari
Jörg-Rüdiger Sack
Christian Scheffer

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Anil Maheshwari, Jörg-Rüdiger Sack, and Christian Scheffer. Approximating the Integral Fréchet Distance. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 26:1-26:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.SWAT.2016.26

Abstract

We present a pseudo-polynomial time (1 + epsilon)-approximation algorithm for computing the integral and average Fréchet distance between two given polygonal curves T_1 and T_2. The running time is in O(zeta^{4}n^4/epsilon^2) where n is the complexity of T_1 and T_2 and zeta is the maximal ratio of the lengths of any pair of segments from T_1 and T_2. Furthermore, we give relations between weighted shortest paths inside a single parameter cell C and the monotone free space axis of C. As a result we present a simple construction of weighted shortest paths inside a parameter cell. Additionally, such a shortest path provides an optimal solution for the partial Fréchet similarity of segments for all leash lengths. These two aspects are related to each other and are of independent interest.
Keywords
  • Fréchet distance
  • partial Fréchet similarity
  • curve matching

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