SIAM Journal on Optimization, Volume 30, Issue 1, Page 1048-1048, January 2020.
On page 2568 of our paper A faster algorithm solving a generalization of isotonic median regression and a class of fused lasso problems, we stated the following: \beginquote Note that Kolmogorov, Pock, and Rolinek in Total variation on a tree also claimed an $O(n\log \log n)$ algorithm for the PL-wFL-O(1) problem. However, the divide-and-conquer technique used in the algorithm requires the sorting of the breakpoints, which adds to the complexity $O(n \log n)$. \endquote This erratum retracts our statement quoted above and corrects the entry relating to this problem in Table 1 of paper A faster algorithm solving a generalization of isotonic median regression and a class of fused lasso problems to read that the run time of the algorithm of paper Total variation on a tree is $O(n\log \log n)$.

中文翻译：

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勘误：一种更快的算法，求解等渗中值回归和一类融合的套索问题

SIAM优化杂志，第30卷，第1期，第1048-1048页，2020年1月。
在本文的第2568页上，一种更快的算法解决了等张中值回归的一般化问题以及一类融合的套索问题，我们指出：\ beginquote请注意，Kolmogorov，Pock和Rolinek在树上的Total变异中也要求$ O （n \ log \ log n）$算法解决PL-wFL-O（1）问题。但是，算法中使用的分治技术需要对断点进行排序，这增加了复杂度$ O（n \ log n）$。\ endquote此勘误表撤回了上面引用的语句，并更正了与本文表1中该问题相关的条目。一种更快的算法，其解决了等张中值回归的一般化问题以及一类融合的套索问题，以读取该算法的运行时间一棵树的总变化量为$ O（n \ log \ log n）$。