Fitting polygonal functions to a set of points in the plane
CVGIP: Graphical Models and Image Processing
A natural metric for curves—computing the distance for polygonal chains and approximation algorithms
STACS 91 Proceedings of the 8th annual symposium on Theoretical aspects of computer science
An O(nlogn) implementation of the Douglas-Peucker algorithm for line simplification
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Cartographic Line Simplification and Polygon CSG Formulae and in O(n log* n) Time
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Approximation of Polygonal Curves with Minimum Number of Line Segments
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A near-linear time guaranteed algorithm for digital curve simplification under the Fréchet distance
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
A heuristic homotopic path simplification algorithm
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Efficient real-time trajectory tracking
The VLDB Journal — The International Journal on Very Large Data Bases
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We study the following variant of the well-known line-simpli-ficationproblem: we are getting a possibly infinite sequence of points p0,p1,p2,... in the plane defining a polygonal path, and as wereceive the points we wish to maintain a simplification of the pathseen so far. We study this problem in a streaming setting, where weonly have a limited amount of storage so that we cannot store all thepoints. We analyze the competitive ratio of our algorithms, allowingresource augmentation: we let our algorithm maintain a simplificationwith 2k (internal) points, and compare the error of oursimplification to the error of the optimal simplification with k points. We obtain the algorithms with O(1) competitive ratio forthree cases: convex paths where the error is measured using theHausdorff distance (or Frechet distance), xy-monotone paths where the error is measured using theHausdorff distance (or Frechet distance), and general paths where the error is measured using theFrechet distance. In the first case the algorithm needs O(k) additionalstorage, and in the latter two cases the algorithm needs O(k2) additional storage.