动态规划的等渗回归

G. Rote
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引用次数: 8

摘要

对于一个给定的数列,我们想要找到一个相同长度的单调递增的数列,它在使差的绝对值的加权和最小的意义上最接近它。一个概念上简单的动态规划方法导致了一个运行时间为O(n logn)的算法。虽然已知其他具有相同运行时间的算法,但我们的算法非常简单。它需要的唯一辅助数据结构是优先级队列。该方法可扩展到其他误差测量。2012 ACM学科分类以人为中心计算→图形绘图。计算数学→图算法
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Isotonic Regression by Dynamic Programming
For a given sequence of numbers, we want to find a monotonically increasing sequence of the same length that best approximates it in the sense of minimizing the weighted sum of absolute values of the differences. A conceptually easy dynamic programming approach leads to an algorithm with running time O(n logn). While other algorithms with the same running time are known, our algorithm is very simple. The only auxiliary data structure that it requires is a priority queue. The approach extends to other error measures. 2012 ACM Subject Classification Human-centered computing → Graph drawings. Mathematics of computing → Graph algorithms
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