Computational geometry: an introduction
Computational geometry: an introduction
Voronoi diagrams and arrangements
Discrete & Computational Geometry
Measuring the resemblance of polygonal curves
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Computing Envelopes in Four Dimensions with Applications
SIAM Journal on Computing
Approximate nearest neighbor algorithms for Frechet distance via product metrics
Proceedings of the eighteenth annual symposium on Computational geometry
Matching Polygonal Curves with Respect to the Fréchet Distance
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Computing the Fréchet distance between simple polygons in polynomial time
Proceedings of the twenty-second annual symposium on Computational geometry
NNCluster: an efficient clustering algorithm for road network trajectories
DASFAA'10 Proceedings of the 15th international conference on Database Systems for Advanced Applications - Volume Part II
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Polygonal chains are fundamental objects in many applications like pattern recognition and protein structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the (continuous/discrete) Fréchet distance. In this paper, for the first time, we consider the Voronoi diagram of polygonal chains in d-dimension under the discrete Fréchet distance. Given a set ${\cal C}$ of npolygonal chains in d-dimension, each with at most kvertices, we prove fundamental properties of such a Voronoi diagram VDF(${\cal C}$). Our main results are summarized as follows. The combinatorial complexity of VD$_F({\cal C})$ is at most O(ndk+ 茂戮驴).The combinatorial complexity of VD$_F({\cal C})$ is at least 茂戮驴(ndk) for dimension d= 1,2; and 茂戮驴(nd(k茂戮驴 1) + 2) for dimension d 2.