Abstract
Given a function y= f(x) in one variable, we consider the problem of computing the single-peaked curve y=φ(x) minimizing the L 2 distance between them. If the input function f is a histogram with O(n) steps or a piecewise linear function with O(n) linear pieces, we design algorithms for computing φ in linear time. We also give an algorithm to approximate f with a function consisting of the minimum number of single-peaked pieces under the condition that each single-peaked piece is within a fixed L 2 distance from the corresponding portion of f.
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Chun, J., Sadakane, K., Tokuyama, T. (2003). Linear Time Algorithm for Approximating a Curve by a Single-Peaked Curve. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_3
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DOI: https://doi.org/10.1007/978-3-540-24587-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20695-8
Online ISBN: 978-3-540-24587-2
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