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446,398
Optimal partitions for eigenvalues
, 2009
"... Abstract. We introduce a new numerical method to approximate partitions of a domain minimizing the sum of DirichletLaplacian eigenvalues of any order. First we prove the equivalence of the original problem and a relaxed formulation based on measures. Using this result, we build a numerical algorith ..."
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Cited by 17 (2 self)
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algorithm to approximate optimal configurations. We describe numerical experiments aimed at studying the asymptotic behavior of optimal partitions with large numbers of cells.
Optimal Partitioning of Multicast Receivers
 In Proceedings of the 8th IEEE International Conference on Network Protocols
, 2000
"... Multicast sessions may have a large number of receivers with heterogeneous reception capacities. To accommodate this heterogeneity, various multirate schemes, based upon the use of layering or replication, have been proposed. We consider in this paper the optimal partitioning of receivers into grou ..."
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Cited by 32 (3 self)
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Multicast sessions may have a large number of receivers with heterogeneous reception capacities. To accommodate this heterogeneity, various multirate schemes, based upon the use of layering or replication, have been proposed. We consider in this paper the optimal partitioning of receivers
Optimizing partitions of percolating graphs
"... The partitioning of random graphs is investigated numerically using \simulated annealing " and \extremal optimization". While generally in an NPhard problem, it is shown that the optimization of the graph partitions is particularly dicult for sparse graphs with average connectivities near ..."
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The partitioning of random graphs is investigated numerically using \simulated annealing " and \extremal optimization". While generally in an NPhard problem, it is shown that the optimization of the graph partitions is particularly dicult for sparse graphs with average connectivities
Optimizing Partitions of Percolating Graphs
 Physica A
, 1999
"... The partitioning of random graphs is investigated numerically using "simulated annealing" and "extremal optimization." While generally an NPhard problem, it is shown that the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivi ..."
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Cited by 1 (0 self)
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The partitioning of random graphs is investigated numerically using "simulated annealing" and "extremal optimization." While generally an NPhard problem, it is shown that the optimization of the graph partitions is particularly difficult for sparse graphs with average
Optimal Partitioning for Spatial Data
, 2000
"... It is desirable to design partitioning techniques that minimize the I/O time incurred during query execution in spatial databases. In this paper, we explore optimal partitioning techniques for spatial data for different types of queries. In particular, we show that hexagonal partitioning has optimal ..."
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It is desirable to design partitioning techniques that minimize the I/O time incurred during query execution in spatial databases. In this paper, we explore optimal partitioning techniques for spatial data for different types of queries. In particular, we show that hexagonal partitioning has
Optimal Partitioning of Multicast Receivers ∗
"... Multicast sessions may have a large number of receivers with heterogeneous reception capacities. To accommodate this heterogeneity, various multirate schemes, based upon the use of layering or replication, have been proposed. We consider in this paper the optimal partitioning of receivers into grou ..."
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Multicast sessions may have a large number of receivers with heterogeneous reception capacities. To accommodate this heterogeneity, various multirate schemes, based upon the use of layering or replication, have been proposed. We consider in this paper the optimal partitioning of receivers
Optimal Partitioning of Sequences
 IEEE TRANSACTIONS ON COMPUTERS
, 1995
"... The problem of partitioning a sequence of n real numbers into p intervals is considered. The goal is to find a partition such that the cost of the most expensive interval measured with a cost function f is minimized. An efficient algorithm which solves the problem in time O(p(n \Gamma p) log p) is d ..."
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Cited by 31 (6 self)
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The problem of partitioning a sequence of n real numbers into p intervals is considered. The goal is to find a partition such that the cost of the most expensive interval measured with a cost function f is minimized. An efficient algorithm which solves the problem in time O(p(n \Gamma p) log p
Optimal Partition Trees
, 2010
"... We revisit one of the most fundamental classes of data structure problems in computational geometry: range searching. Back in SoCG’92, Matouˇsek gave a partition tree method for ddimensional simplex range searching achieving O(n) space and O(n 1−1/d) query time. Although this method is generally be ..."
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Cited by 24 (2 self)
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(n) space, and O(n1−1/d) query time with high probability. Our method has several advantages: • It is conceptually simpler than Matouˇsek’s SoCG’92 method. Our partition trees satisfy many ideal properties (e.g., constant degree, optimal crossing number at almost all layers, and disjointness of the children
Computing the optimal partition of variables . . .
, 2004
"... partition of variables reduces the computational cost in curve following to the minimum. However, finding the optimal variable partition is likely an NP hard problem. An Consider a system of polynomial equations Applied Mathematics and Computation xxx (2004) xxx–xxx www.elsevier.com/locate/amc ARTI ..."
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partition of variables reduces the computational cost in curve following to the minimum. However, finding the optimal variable partition is likely an NP hard problem. An Consider a system of polynomial equations Applied Mathematics and Computation xxx (2004) xxx–xxx www
Cluster Ensembles  A Knowledge Reuse Framework for Combining Multiple Partitions
 Journal of Machine Learning Research
, 2002
"... This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse&ap ..."
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Cited by 589 (21 self)
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This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse
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