A linear time algorithm with minimum link paths inside a simple polygon
Computer Vision, Graphics, and Image Processing
Fitting polygonal functions to a set of points in the plane
CVGIP: Graphical Models and Image Processing
Randomized optimal algorithm for slope selection
Information Processing Letters
An Expander-Based Approach to Geometric Optimization
SIAM Journal on Computing
Approximation of Polygonal Curves with Minimum Number of Line Segments
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
Plane Sweep Algorithms for the Polygonal Approximation Problems with Applications
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Streaming Algorithms for Line Simplification
Discrete & Computational Geometry
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We study the problem of approximating a function F : R → R by a piecewise-linear function F when the values of F at {x1,...,xn} are given by a discrete probability distribution. Thus, for each xi we are given a discrete set yi,1,...,yi, mi of possible function values with associated probabilities pi,j such that Pr[F(xi) = yi,j] = pi,j. We define the error of F as error(F, F) = maxi=1n E[|F(xi) - F(xi)|]. Let m = Σi=1n mi be the total number of potential values over all F(xi). We obtain the following two results: (i) an O(m) algorithm that, given F and a maximum error ε, computes a function F with the minimum number of links such that error(F, F) ≤ ε; (ii) an O(n4/3+δ+m log n) algorithm that, given F, an integer value 1 ≤ k ≤ n and any δ 0, computes a function F of at most k links that minimizes error(F, F).