A complexity analysis of Policy Iteration through combinatorial matrices arising from Unique Sink Orientations
نویسندگان
چکیده
منابع مشابه
A complexity analysis of Policy Iteration through combinatorial matrices arising from Unique Sink Orientations
We construct a family of Order-Regular matrices of size m×n such that m ∼ Ω ( 10 √ 33 n) . Previously Order-Regular matrices were known only for m ∼ O (√ 2 n) .
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A unique sink orientation (USO) is an orientation of the n-dimensional cube graph (n-cube) such that every face (subcube) has a unique sink. The number of unique sink orientations is nΘ(2 n) [13]. If a cube orientation is not a USO, it contains a pseudo unique sink orientation (PUSO): an orientation of some subcube such that every proper face of it has a unique sink, but the subcube itself hasn...
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Unique-sink orientations (USOs) are an abstract class of orientations of the ncube graph. We consider some classes of USOs that are of interest in connection with the linear complementarity problem. We summarise old and show new lower and upper bounds on the sizes of some such classes. Furthermore, we provide a characterisation of K-matrices in terms of their corresponding USOs.
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Suppose we are given (the edge graph of) an dimensional hypercube with its edges oriented so that every face has a unique sink. Such an orientation is called a unique sink orientation, and we are interested in finding the unique sink of the whole cube, when the orientation is given implicitly. The basic operation available is the socalled vertex evaluation, where we can access an arbitrary vert...
متن کاملUnique Sink Orientations of Cubes
Subject of this thesis is the theory of unique sink orientations of cubes. Such orientations are suitable to model problems from different areas of combinatorial optimization. In particular, unique sink orientations are closely related to the running time of the simplex algorithm. In the following, we try to answer three main questions: How can optimization problems be translated into the frame...
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2017
ISSN: 1570-8667
DOI: 10.1016/j.jda.2017.04.004