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Shanqi Pang
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Binary space partitions of orthogonal subdivisions
Proceedings of the twentieth annual symposium on Computational geometry, 2004Summary: 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
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On the orthogonal Grünbaum partition problem in dimension three
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
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Partitioning and separating sets of orthogonal polygons
Information Sciences, 1987A 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
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Computing conforming partitions of orthogonal polygons with minimum stabbing number
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Stephane Durocher, Saeed Mehrabi
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The structure of optimal partitions of orthogonal polygons into fat rectangles
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Joseph O'Rourke
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Partitioning Orthogonal Histograms into Rectangular Boxes
2018The 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
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Set-partition methods and orthogonal designs
2010 IEEE International Symposium on Information Theory, 2010Space-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
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.
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Variation partitioning involving orthogonal spatial eigenfunction submodels
Ecology, 2012When 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
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