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Linear Time Algorithm for Approximating a Curve by a Single-Peaked Curve

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Abstract

Given a function y = f(x) in one variable, we consider the problem of computing the single-peaked (unimodal) 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 unimodal pieces under the condition that each unimodal piece is within a fixed L2-distance from the corresponding portion of f.

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Authors and Affiliations

  1. GSIS, Tohoku University, Sendai, Japan

    Jinhee Chun & Takeshi Tokuyama

  2. Graduate School of System Information Science, Kyushu University, Hakozaki, Japan

    Kunihiko Sadakane

Authors
  1. Jinhee Chun
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  2. Kunihiko Sadakane
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  3. Takeshi Tokuyama
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Corresponding authors

Correspondence to Jinhee Chun, Kunihiko Sadakane or Takeshi Tokuyama.

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Chun, J., Sadakane, K. & Tokuyama, T. Linear Time Algorithm for Approximating a Curve by a Single-Peaked Curve. Algorithmica 44, 103–115 (2006). https://doi.org/10.1007/s00453-005-1201-y

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  • DOI: https://doi.org/10.1007/s00453-005-1201-y

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