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arXiv · 1507.02226

L infinity Isotonic Regression for Linear, Multidimensional, and Tree Orders

Quentin F. Stout
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Abstract

Algorithms are given for determining $L_\infty$ isotonic regression of weighted data. For a linear order, grid in multidimensional space, or tree, of $n$ vertices, optimal algorithms are given, taking $\Theta(n)$ time. These improve upon previous algorithms by a factor of $\Omega(\log n)$. For vertices at arbitrary positions in $d$-dimensional space a $\Theta(n \log^{d-1} n)$ algorithm employs iterative sorting to yield the functionality of a multidimensional structure while using only $\Theta(n)$ space. The algorithms utilize a new non-constructive feasibility test on a rendezvous graph, with bounded error envelopes at each vertex.

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Quentin F. Stout. 2015-07-08. L infinity Isotonic Regression for Linear, Multidimensional, and Tree Orders. https://arxiv.org/abs/1507.02226

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