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Construction of Asymmetric Orthogonal Arrays of Strength t from Orthogonal Partition of Small Orthogonal Arrays

open access: yesIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2018
Shanqi Pang
exaly   +3 more sources
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Binary space partitions of orthogonal subdivisions

Proceedings of the twentieth annual symposium on Computational geometry, 2004
Summary: We consider the problem of constructing Binary Space Partitions (BSPs) for orthogonal subdivisions (space-filling packings of boxes) in \(d\)-space. We show that a subdivision with \(n\) boxes can be refined into a BSP of size \(O(n^{(d+1)/{3}})\) for all \(d \geq 3\) and that such a partition can be computed in time \({O(K\log n)}\), where ...
John Hershberger 0001   +2 more
openaire   +3 more sources

On the orthogonal Grünbaum partition problem in dimension three

open access: yesComputational Geometry: Theory and Applications
Grünbaum's equipartition problem asked if for any measure $μ$ on $\mathbb{R}^d$ there are always $d$ hyperplanes which divide $\mathbb{R}^d$ into $2^d$ $μ$-equal parts. This problem is known to have a positive answer for $d\le 3$ and a negative one for $d\ge 5$. A variant of this question is to require the hyperplanes to be mutually orthogonal.
Edgardo Roldán-Pensado   +1 more
exaly   +5 more sources

Partitioning and separating sets of orthogonal polygons

Information Sciences, 1987
A geometrical object in the plane is said to be orthogonal if its edges are either vertical or horizontal. A polygon is called orthoconvex if for every vertical-or-horizontal segment, its two endpoints lying in the polygon implies the whole segment lying in the polygon.
Thomas Ottmann   +2 more
openaire   +1 more source

Computing conforming partitions of orthogonal polygons with minimum stabbing number

open access: yesTheoretical Computer Science, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephane Durocher, Saeed Mehrabi
exaly   +4 more sources

The structure of optimal partitions of orthogonal polygons into fat rectangles

open access: yesComputational Geometry: Theory and Applications, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joseph O'Rourke
exaly   +4 more sources

Partitioning Orthogonal Histograms into Rectangular Boxes

2018
The problem of partitioning an orthogonal polyhedron into a minimum number of boxes was shown to be NP-hard in 1991, but no approximability result is known except for a 4-approximation algorithm for 3D-histograms. In this paper we broaden the understanding of the 3D-histogram partitioning problem.
Therese Biedl   +5 more
openaire   +1 more source

Set-partition methods and orthogonal designs

2010 IEEE International Symposium on Information Theory, 2010
Space-time block codes based on orthogonal designs are useful from practical point of view as these codes admit symbol-by-symbol maximum-likelihood decoding and also achieve full diversity. Though the square orthogonal designs have been studied quite extensively, there is very little progress in the area of non-square orthogonal designs.
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Partition functions from orthogonal and symplectic group invariants

open access: yesElectronic Notes in Discrete Mathematics, 2017
We introduce a new class of graph parameters coming from invariants of the orthosymplectic group, which we call mixed partition functions. This class strictly contains partition functions of edge-coloring models and we give a characterization of this class by means of rank growth of associated connection matrices.
Regts, G., Sevenster, B.
exaly   +4 more sources

Variation partitioning involving orthogonal spatial eigenfunction submodels

Ecology, 2012
When partitioning the variation of univariate or multivariate ecological data with respect to several submodels of spatial eigenfunctions (e.g., Moran's eigenvector maps, MEM) acting as explanatory data, a problem occurs: although the submodels are constructed to be orthogonal to one another, the partitioning based on adjusted R2 statistics produces ...
Pierre, Legendre   +2 more
openaire   +2 more sources

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