منابع مشابه
Strict L∞ Isotonic Regression
Given a function f and weightsw on the vertices of a directed acyclic graphG, an isotonic regression of (f, w) is an order-preserving real-valued function that minimizes the weighted distance to f among all order-preserving functions. When the distance is given via the supremum norm there may be many isotonic regressions. One of special interest is the strict isotonic regression, which is the l...
متن کاملWeighted L∞ isotonic regression
Algorithms are given for determining weighted L∞ isotonic regressions satisfying order constraints given by a directed acyclic graph (dag) with n vertices andm edges. An algorithm is given takingΘ(m log n) time for the general case. However, it relies on parametric search, so a practical approach is introduced, based on calculating prefix solutions. While not as fast in the general case, for li...
متن کاملAlgorithms for L∞ Isotonic Regression
This paper gives algorithms for determining L∞ weighted isotonic regressions satisfying order constraints given by a DAG with n vertices and m edges. Throughout, topological sorting plays an important role. A modification to an algorithm of Kaufman and Tamir gives an algorithm taking Θ(m log n) time for the general case, improving upon theirs when the graph is sparse. When the regression values...
متن کاملL∞ Isotonic Regression for Linear, Multidimensional, and Tree Orders
Algorithms are given for determining L∞ isotonic regression of weighted data. For a linear order, grid in multidimensional space, or tree, of n vertices, optimal algorithms are given, taking Θ(n) time. These improve upon previous algorithms by a factor of Ω(log n). For vertices at arbitrary positions in d-dimensional space a Θ(n log n) algorithm employs iterative sorting to yield the functional...
متن کاملL infinity Isotonic Regression for Linear, Multidimensional, and Tree Orders
Algorithms are given for determining L∞ isotonic regression of weighted data where the independent set is n vertices in multidimensional space or in a rooted tree. For a linear order, or, more generally, a grid in multidimensional space, an optimal algorithm is given, taking Θ(n) time. For vertices at arbitrary locations in d-dimensional space a Θ(n log n) algorithm employs iterative sorting to...
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ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2011
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-011-9865-8