Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Maximin location of convex objects in a polygon and related dynamic Voronoi diagrams
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Computing the minimum Hausdorff distance for point sets under translation
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
The upper envelope of Voronoi surfaces and its applications
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
An efficiently computable metric for comparing polygonal shapes
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Approximate Geometric Pattern Matching Under Rigid Motions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric pattern matching: a performance study
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximate congruence in nearly linear time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Reliable and Efficient Pattern Matching Using an Affine Invariant Metric
International Journal of Computer Vision
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate congruence in nearly linear time
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Compact Voronoi Diagrams for Moving Convex Polygons
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Exact Point Pattern Matching and the Number of Congruent Triangles in a Three-Dimensional Pointset
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Hausdorff distance under translation for points and balls
Proceedings of the nineteenth annual symposium on Computational geometry
Content based retrieval of VRML objects: an iterative and interactive approach
Proceedings of the sixth Eurographics workshop on Multimedia 2001
Approximate Nearest Neighbor Algorithms for Hausdorff Metrics via Embeddings
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Java applets for the dynamic visualization of Voronoi diagrams
Computer Science in Perspective
Buddy tracking - efficient proximity detection among mobile friends
Pervasive and Mobile Computing
Information Processing Letters
ACM Transactions on Database Systems (TODS)
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
An incremental Hausdorff distance calculation algorithm
Proceedings of the VLDB Endowment
Superposition and Alignment of Labeled Point Clouds
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximate one-to-one point pattern matching
Journal of Discrete Algorithms
Fast and exact network trajectory similarity computation: a case-study on bicycle corridor planning
Proceedings of the 2nd ACM SIGKDD International Workshop on Urban Computing
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We show that the dynamic Voronoi diagram of k sets of points in the plane, where each set consists of m points moving rigidly, has complexity O(n2k2&lgr;s(k)) for some fixed s, where &lgr;s(n) is the maximum length of a (n, s) Davenport-Schinzel sequence. This improves the result of Aonuma et al., who show an upper bound of O(n3k4 log* k) for the complexity of such Voronoi diagrams. We then apply this result to the problem of finding the minimum Hausdorff distance between two point sets in the plane under Euclidean motion. We show that this distance can be computed in time O((m + n)6 log (mn)), where the two sets contain m and n points respectively.