IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximate nearest neighbor algorithms for Frechet distance via product metrics
Proceedings of the eighteenth annual symposium on Computational geometry
Scaling up Dynamic Time Warping to Massive Dataset
PKDD '99 Proceedings of the Third European Conference on Principles of Data Mining and Knowledge Discovery
Pattern Matching for Spatial Point Sets
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Journal of Algorithms
Comparison of Distance Measures for Planar Curves
Algorithmica
Approximately matching polygonal curves with respect to the Fréchet distance
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Optimization of subsequence matching under time warping in time-series databases
Proceedings of the 2005 ACM symposium on Applied computing
On map-matching vehicle tracking data
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Computing the Fréchet distance between piecewise smooth curves
Computational Geometry: Theory and Applications
Journal of Mathematical Imaging and Vision
Fréchet distance for curves, revisited
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Computing the Fréchet distance between simple polygons
Computational Geometry: Theory and Applications
Walking your dog in the woods in polynomial time
Proceedings of the twenty-fourth annual symposium on Computational geometry
Detecting single file movement
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Detecting Commuting Patterns by Clustering Subtrajectories
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Fréchet Distance Problems in Weighted Regions
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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
Finding long and similar parts of trajectories
Computational Geometry: Theory and Applications
Improved algorithms for partial curve matching
ESA'11 Proceedings of the 19th European conference on Algorithms
Jaywalking your dog: computing the Fréchet distance with shortcuts
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Partial matching between surfaces using fréchet distance
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Constructing street networks from GPS trajectories
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Low cost positioning by matching altitude readings with crowd-sourced route data
Proceedings of the 10th International Conference on Advances in Mobile Computing & Multimedia
Computational Geometry: Theory and Applications
Measuring similarity between curves on 2-manifolds via homotopy area
Proceedings of the twenty-ninth annual symposium on Computational geometry
Similarity of polygonal curves in the presence of outliers
Computational Geometry: Theory and Applications
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Curve matching is a fundamental problem that occurs in many applications. In this paper, we study the problem of measuring partial similarity between curves. Specifically, given two curves, we wish to maximize the total length of subcurves that are close to each other, where closeness is measured by the Fréchet distance, a common distance measure for curves. The resulting maximal length is called the partial Fréchet similarity between the two input curves. Given two polygonal curves P and Q in Rd of size m and n, respectively, we present the first exact algorithm that runs in polynomial time to compute fδ(P, Q), the partial Fréchet similarity between P and Q, under the L1 and L∞ norms. Specifically, we formulate the problem of computing fδ(P, Q) as a longest path problem, and solve it in O(mn(m + n) log(mn)) time, under the L1 or L∞ norm, using a "shortest-path map" type decomposition. To the best of our knowledge, this is the first paper to study this natural definition of partial curve similarity in the continuous setting (with all points in the curve considered), and present a polynomial-time exact algorithm for it.