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8,671
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique
Learnability and the VapnikChervonenkis dimension
, 1989
"... Valiant’s learnability model is extended to learning classes of concepts defined by regions in Euclidean space E”. The methods in this paper lead to a unified treatment of some of Valiant’s results, along with previous results on distributionfree convergence of certain pattern recognition algorith ..."
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Cited by 727 (22 self)
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Valiant’s learnability model is extended to learning classes of concepts defined by regions in Euclidean space E”. The methods in this paper lead to a unified treatment of some of Valiant’s results, along with previous results on distributionfree convergence of certain pattern recognition
Greedy Randomized Adaptive Search Procedures
, 2002
"... GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phas ..."
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Cited by 647 (82 self)
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GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search
The Ant System: Optimization by a colony of cooperating agents
 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICSPART B
, 1996
"... An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call Ant System. We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation ..."
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Cited by 1300 (46 self)
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An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call Ant System. We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed
How Iris Recognition Works
, 2003
"... Algorithms developed by the author for recognizing persons by their iris patterns have now been tested in six field and laboratory trials, producing no false matches in several million comparison tests. The recognition principle is the failure of a test of statistical independence on iris phase st ..."
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Cited by 509 (4 self)
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structure encoded by multiscale quadrature wavelets. The combinatorial complexity of this phase information across different persons spans about 244 degrees of freedom and generates a discrimination entropy of about 3.2 bits/mm over the iris, enabling realtime decisions about personal identity
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 633 (38 self)
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Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work
Combinatorial results for semigroups of orderpreserving partial transformations
 J. Algebra
"... Let PCn be the semigroup of all decreasing and orderpreserving partial transformations of a finite chain. It is shown that PCn  = rn, where rn is the large (or double) Schröder number. Moreover, the total number of idempotents of PCn is shown to be (3 n + 1)/2. 1 ..."
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Cited by 11 (4 self)
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Let PCn be the semigroup of all decreasing and orderpreserving partial transformations of a finite chain. It is shown that PCn  = rn, where rn is the large (or double) Schröder number. Moreover, the total number of idempotents of PCn is shown to be (3 n + 1)/2. 1
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 603 (20 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
PROOF OF TWO COMBINATORIAL RESULTS ARISING IN ALGEBRAIC GEOMETRY
, 805
"... Abstract. For a labeled tree on the vertex set [n]: = {1, 2,...,n}, define the direction of each edge ij as i → j if i < j. The indegree sequence λ = 1 e1 2 e2... is then a partition of n −1. Let aλ be the number of trees on [n] with indegree sequence λ. In a recent paper (arXiv:0706.2049v2) Cott ..."
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Cited by 2 (0 self)
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Abstract. For a labeled tree on the vertex set [n]: = {1, 2,...,n}, define the direction of each edge ij as i → j if i < j. The indegree sequence λ = 1 e1 2 e2... is then a partition of n −1. Let aλ be the number of trees on [n] with indegree sequence λ. In a recent paper (arXiv:0706.2049v2) Cotterill stumbled across the following two remarkable formulas aλ =
Matching points with geometric objects: Combinatorial results
 Proc. 8th Jap. Conf. Discrete Comput. Geometry (JCDCG’04
, 2005
"... Abstract. Given a class C of geometric objects and a point set P,aCmatching of P is a set M = {C1,...,Ck} of elements of C such that every Ci contains exactly two elements of P. If all the elements of P belong to some Ci, M is called a perfect matching; if in addition all the elements of M are pairw ..."
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Cited by 2 (0 self)
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Abstract. Given a class C of geometric objects and a point set P,aCmatching of P is a set M = {C1,...,Ck} of elements of C such that every Ci contains exactly two elements of P. If all the elements of P belong to some Ci, M is called a perfect matching; if in addition all the elements of M are pairwise disjoint we say that this matching M is strong. In this paper we study the existence and characteristics of Cmatchings for point sets on the plane when C is the set of circles or the set of isothetic squares on the plane. 1
Results 1  10
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