Given a function y = f(x) in one variable, we consider the problem of computing the single-peaked curve y = φ(x) minimizing the L2 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 L2 distance from the corresponding portion of f. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Chun, J., Sadakane, K., & Tokuyama, T. (2003). Linear time algorithm for approximating a curve by a single-peaked curve. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2906, 6–15. https://doi.org/10.1007/978-3-540-24587-2_3
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