Streaming algorithms for line simplification

We study the following variant of the well-known line-simplification problem: we are getting a possibly infinite sequence of points p0, p1, p2, . . . in the plane defining a polygonal path, and as we receive the points we wish to maintain a simplification of the path seen so far. We study this problem in a streaming setting, where we only have a limited amount of storage so that we cannot store all the points. We analyze the competitive ratio of our algorithms, allowing resource augmentation: we let our algorithm maintain a simplification with 2k (internal) points, and compare the error of our simplification to the error of the optimal simplification with k points. We obtain the algorithms with O(1) competitive ratio for three cases: convex paths where the error is measured using the Hausdorff distance (or Fr

• Type: Conference
• Year: 2007
• Where: COMPGEOM
• Authors: Mohammad Ali Abam, Mark de Berg, Peter Hachenberger, Alireza Zarei
• Keywords: Competitive Ratio, COMPGEOM 2007, Discrete Geometry, Fr´echet Distance, Simplification