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and the SumofSquares Partition Problem
, 2004
"... Abstract We propose a simple game for modeling containment of the spread of viruses in a graph of nnodes. Each node must choose to either install antivirus software at some known cost C, or riskinfection and a loss L if a virus that starts at a random initial point in the graph can reach itwithout ..."
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that the problem can be reduced to a previously unconsidered combinatorial problem that we call the sumofsquares partition problem.Using a greedy algorithm based on sparse cuts, we show that this problem can be approximated to within a factor of O(log2 n), giving the same approximation ratio for the inoculation
Inoculation Strategies for Victims of Viruses and the SumofSquares Partition Problem
 PROCEEDINGS OF THE 16TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2005
"... We propose a simple game for modeling containment of the spread of viruses in a graph of n nodes. Each node must choose to either install antivirus software at some known cost C, or risk infection and a loss L if a virus that starts at a random initial point in the graph can reach it without being ..."
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Cited by 67 (2 self)
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that the problem can be reduced to a previously unconsidered combinatorial problem that we call the sumofsquares partition problem. Using a greedy algorithm based on sparse cuts, we show that this problem can be approximated to within a factor of O(log² n), giving the same approximation ratio for the inoculation
Inoculation Strategies for Victims of Viruses and the SumofSquares Partition Problem
, 2004
"... ..."
On the SumofSquares Algorithm for Bin Packing
, 2000
"... In this paper we present a theoretical analysis of the deterministic online Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) ar ..."
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Cited by 126 (6 self)
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In this paper we present a theoretical analysis of the deterministic online Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s
Noncommutative circuits and the sumofsquares problem
 J. Amer. Math. Soc
"... 1.1. Noncommutative computation. Arithmetic complexity theory studies the computation of formal polynomials over some field or ring. Most of this theory is concerned with the computation of commutative polynomials. The basic model of computation is that of an arithmetic circuit. Despite decades of ..."
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Cited by 2 (2 self)
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1.1. Noncommutative computation. Arithmetic complexity theory studies the computation of formal polynomials over some field or ring. Most of this theory is concerned with the computation of commutative polynomials. The basic model of computation is that of an arithmetic circuit. Despite decades of work, the best
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
Irrelevant Features and the Subset Selection Problem
 MACHINE LEARNING: PROCEEDINGS OF THE ELEVENTH INTERNATIONAL
, 1994
"... We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small highaccuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features ..."
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Cited by 741 (26 self)
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We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small highaccuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features
Clustering by Maximizing SumofSquared Separation Distance
"... Maximizing the separating margin is crucial for the good generalization performance of Support Vector Machines (SVMs). Analogous to the definition of separation distance or separating margin in SVMs, we propose a definition on separation distance in clustering tasks when a hyperplane is used to sepa ..."
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Maximizing the separating margin is crucial for the good generalization performance of Support Vector Machines (SVMs). Analogous to the definition of separation distance or separating margin in SVMs, we propose a definition on separation distance in clustering tasks when a hyperplane is used to separate clusters. For given training data and a given metric distance, by maximizing the proposed separation distance, our clustering algorithm constructs an “optimal” hyperplane that can be applied to unseen data in the future. The resulting hyperplane corresponds to a nonlinear decision boundary in the input feature space through an appropriate distance feature mapping. A graphtheoretic perspective of the proposed method is discussed. In particular, we show that, under certain conditions, the proposed clustering algorithm is equivalent to a spectral relaxed graph cut. Extensive experimental results are provided to validate the method.
Hypercontractivity, SumofSquares Proofs, and their Applications
, 2013
"... We study the computational complexity of approximating the 2toq norm of linear operators (defined as ‖A‖2→q = maxv�0‖Av‖q/‖v‖2) for q> 2, as well as connections between this question and issues arising in quantum information theory and the study of Khot’s Unique Games Conjecture (UGC). We show ..."
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close variant of the UGC. We also show that such a good approximation can be computed in exp(n 2/q) time, thus obtaining a different proof of the known subexponential algorithm for SmallSet Expansion. 2. Constant rounds of the “Sum of Squares ” semidefinite programing hierarchy certify an upper bound
Results 1  10
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