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319
Stable Minimum Space Partitioning in Linear Time
, 1992
"... In the stable 01 sorting problem the task is to sort an array of n elements with two distinct values such that equal elements retain their relative input order. ..."
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Cited by 17 (4 self)
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In the stable 01 sorting problem the task is to sort an array of n elements with two distinct values such that equal elements retain their relative input order.
Partitioned EliasFano Indexes
"... The EliasFano representation of monotone sequences has been recently applied to the compression of inverted indexes, showing excellent query performance thanks to its efficient random access and search operations. While its space occupancy is competitive with some stateoftheart methods such as ..."
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Cited by 3 (2 self)
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. For the latter case we introduce a lineartime optimization algorithm which identifies the minimumspace partition up to an arbitrarily small approximation factor. We show that our partitioned EliasFano indexes offer significantly better compression than plain EliasFano, while preserving their query time
Multiview Stereo via Volumetric Graphcuts and Occlusion Robust PhotoConsistency
, 2007
"... This paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimisation using Graphcuts. Our approach is to seek the optimal partitioning of 3D space into two regions labelled as ‘object’ and ‘empty’ under a cost functional ..."
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Cited by 189 (9 self)
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This paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimisation using Graphcuts. Our approach is to seek the optimal partitioning of 3D space into two regions labelled as ‘object’ and ‘empty’ under a cost
Graph Partition by SwendsenWang Cuts
, 2003
"... Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimumcut using the maximum flow algorithm. This paper presents a third major a ..."
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Cited by 75 (14 self)
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Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimumcut using the maximum flow algorithm. This paper presents a third major
Sorting Multisets Stably in Minimum Space
, 1994
"... We consider the problem of sorting a multiset of size n containing m distinct elements, where the ith distinct element appears n i times. Under the assumption that our model of computation allows only the operations of comparing elements and moving elements in the memory, \Omega (n log n \Gamm ..."
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recursive step the median is chosen as the partitioning element. To obtain a stable minimum space implementation, we develop lineartime inplace algorithms for the following problems, which have interest of their own: Stable unpartitioning: Assume that an nelement array A is stably partitioned
The minimum principle for hybrid systems with partitioned state space and unspecified discrete state sequence
 in Proc. of the 49th IEEE Conf. on Decision and Control
, 2010
"... Abstract — The hybrid minimum principle (HMP) gives necessary conditions to be satisfied for optimal solutions of a hybrid dynamical system. In particular, the HMP accounts for autonomous switching between discrete states that occurs whenever the trajectory hits switching manifolds. In this paper, t ..."
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Cited by 5 (2 self)
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, the existing HMP is extended for hybrid systems with partitioned state space to provide necessary conditions for optimal trajectories that pass through an intersection of switching manifolds. This extension is especially useful for the numerical solution of hybrid optimal control problems as it allows
On Partitions of Finite vector Spaces
, 2009
"... In this note, we give a new necessary condition for the existence of nontrivial partitions of a finite vector space. Precisely, we prove that the number of the subspaces of minimum dimension t of a nontrivial partition of Vn(q) is greater than or equal to q + t. Moreover, we give some extensions o ..."
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Cited by 1 (0 self)
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In this note, we give a new necessary condition for the existence of nontrivial partitions of a finite vector space. Precisely, we prove that the number of the subspaces of minimum dimension t of a nontrivial partition of Vn(q) is greater than or equal to q + t. Moreover, we give some extensions
Circular Partitions with Applications to Visualization and Embeddings
, 2008
"... We introduce a hierarchical partitioning scheme of the Euclidean plane, called circular partitions. Such a partition consists of a hierarchy of convex polygons, each having small aspect ratio, and satisfying specified volume constraints. We apply these partitions to obtain a natural extension of the ..."
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Cited by 7 (4 self)
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these relaxed partitions to obtain improved approximation algorithms for embedding ultrametrics into ddimensional Euclidean space. In particular, we give a polylog(∆)approximation algorithm for embedding npoint ultrametrics into R d with minimum distortion ( ∆ denotes the spread of the metric
A New Approach to Fuzzy Partitioning
 In Proc. of the Joint 9th IFSA World Congress and 20th NAFIPS Int. Conf
, 2001
"... Fuzzy clustering algorithms like the popular fuzzy cmeans algorithm (FCM) are frequently used to automatically divide up the data space into fuzzy granules (fuzzy vector quantization). In the context of fuzzy systems, in order to be intuitive and meaningful to the user, the fuzzy membership function ..."
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Cited by 6 (1 self)
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FCM using distances to the Voronoi cell of the cluster rather than using distances to the cluster prototypes. In consequence, the resulting partitions of the modified algorithm are much closer to those of the crisp original methods. The membership functions can be generalized to a fuzzified minimum
Partitioning Nominal Attributes in Decision Trees
 DATA MINING AND KNOWLEDGE DISCOVERY
, 1999
"... To find the optimal branching of a nominal attribute at a node in an Lary decision tree, one is often forced to search over all possible Lary partitions for the one that yields the minimum impurity measure. For binary trees (L =2) when there are just two classes a shortcut search is possible th ..."
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Cited by 3 (0 self)
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To find the optimal branching of a nominal attribute at a node in an Lary decision tree, one is often forced to search over all possible Lary partitions for the one that yields the minimum impurity measure. For binary trees (L =2) when there are just two classes a shortcut search is possible
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