Abstract
Given an n-vertex polygonal curve P = [p 1, p 2, . . ., p n] in the 2-dimensional space R 2, we consider the problem of approximating P by finding another polygonal curve P′ = [p′ 1, p′ 2, . . ., p′ m] of m vertices in R 2 such that the vertex sequence of P′ is an ordered subsequence of the vertices along P. The goal is to either minimize the size m of P′ for a given error tolerance ε (called the min-# problem), or minimize the deviation error ε between P and P′ for a given size m of P′ (called the min-ε problem). We present useful techniques and develop a number of efficient algorithms for solving the 2-D min-# and min-ε problems under two commonly-used error criteria for curve approximations. Our algorithms improve substantially the space bounds of the previously best known results on the same problems while maintain the same time bounds as those of the best known algorithms.
This research was supported in part by the National Science Foundation under Grant CCR-9623585.
This author was supported in part by a fellowship of the Center for Applied Mathematics of the University of Notre Dame.
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Chen, D.Z., Daescu, O. (1998). Space-Efficient Algorithms for Approximating Polygonal Curves in Two Dimensional Space. In: Hsu, WL., Kao, MY. (eds) Computing and Combinatorics. COCOON 1998. Lecture Notes in Computer Science, vol 1449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68535-9_8
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DOI: https://doi.org/10.1007/3-540-68535-9_8
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