动态时间弯曲下的快速二进制均值计算
Faster Binary Mean Computation Under Dynamic Time Warping
摘要：
许多共识串问题都是基于汉明距离的。我们用更灵活的（例如，容易处理不同的输入字符串长度）动态时间弯曲距离，最好从时间序列挖掘中的应用中得知。这样做，我们研究的问题，找到一个平均字符串，最大限度地减少（平方）动态时间弯曲距离的总和到一组给定的输入字符串。虽然这个问题是已知的NP-难（即使是字符串的三个元素的字母表），我们解决的二进制字母表的情况下，这是已知的多项式时间可解的。我们显着改善了以前已知的算法在最坏情况下的运行时间。此外，我们还展示了我们的算法在实验中与现实世界和合成数据的实用性。最后，我们确定了在线性时间内可解的特殊情况（例如，找到只有两个二进制输入字符串的平均值），并报告了一些关于最佳平均值的组合特性的经验发现。
英文摘要：
Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time series mining. Doing so, we study the problem of finding a mean string that minimizes the sum of (squared) dynamic time warping distances to a given set of input strings. While this problem is known to be NP-hard (even for strings over a three-element alphabet), we address the binary alphabet case which is known to be polynomial-time solvable. We significantly improve on a previously known algorithm in terms of worst-case running time. Moreover, we also show the practical usefulness of one of our algorithms in experiments with real-world and synthetic data. Finally, we identify special cases solvable in linear time (e.g., finding a mean of only two binary input strings) and report some empirical findings concerning combinatorial properties of optimal means.
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