Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Pattern matching for sets of segments
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Geometric shape matching and drug design
Geometric shape matching and drug design
Fréchet distance for curves, revisited
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Voronoi Diagram of Polygonal Chains under the Discrete Fréchet Distance
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Computer Vision and Image Understanding
Go with the flow: the direction-based fréchet distance of polygonal curves
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Mining spatial trajectories using non-parametric density functions
MLDM'11 Proceedings of the 7th international conference on Machine learning and data mining in pattern recognition
Similarity in (spatial, temporal and) spatio-temporal datasets
Proceedings of the 15th International Conference on Extending Database Technology
A polynomial time solution for protein chain pair simplification under the discrete fréchet distance
ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
Protein Chain Pair Simplification under the Discrete Fréchet Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We provide the first algorithm for matching two polygonal curves P and Q under translations with respect to the FrÉchet distance. If P and Q consist of m and n segments, respectively, the algorithm has runtime O((mn)3(m+n)2 log(m+n)). We also present an algorithm giving an approximate solution as an alternative. To this end, we generalize the notion of a reference point and observe that all reference points for the Hausdorff distance are also reference points for the FrÉchet distance. Furthermore we give a new reference point that is substantially better than all known reference points for the Hausdorff distance. These results yield a (1 + Ɛ)-approximation algorithm for the matching problem that has runtime O(Ɛ-2mn).