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Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices,the Isotonic Regression of $y$ is a vector $x$ that respects the partial orderdescribed by $G,$ and minimizes $||x-y||,$ for a specified norm. This papergives improved algorithms for computing the Isotonic Regression for allweighted $\ell_{p}$-norms with rigorous performance guarantees. Our algorithmsare quite practical, and their variants can be implemented to run fast inpractice.

Fast, Provable Algorithms for Isotonic Regression in all $\ell_{p}$-norms