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Treetree matrices and other combinatorial problems from taxonomy
 NATIONAL RESEARCH INSTITUTE FOR MATHEMATICS AND COMPUTER SCIENCE IN THE
, 1995
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An Eigendecomposition Approach to Weighted Graph Matching Problems
, 1988
"... This paper discusses an approximate solution to the weighted graph matching prohlem (WGMP) for both undirected and directed graphs. The WGMP is the problem of f inding the optimum matching between two weighted graphs, which are graphs with weights at each arc. The proposed method employs an analytic ..."
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Cited by 202 (0 self)
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an analytic, instead of a combinatorial or iterative, approach to the opt imum matching problem of such graphs. By using the eigendecompositions of the adjacency matrices (in the case of the undirected graph matching problem) or some Hermitian matrices derived from the adjacency matrices (in the case
Parallel family trees for transfer matrices . . .
, 2014
"... The computational cost of transfer matrix methods for the Potts model is related to the question into how many ways can two layers of a lattice be connected?. Answering the question leads to the generation of a combinatorial set of lattice configurations. This set defines the configuration space of ..."
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of the problem, and the smaller it is, the faster the transfer matrix can be computed. The configuration space of generic (q, v) transfer matrix methods for strips is in the order of the Catalan numbers, which grows asymptotically as O(4m) where m is the width of the strip. Other transfer matrix methods with a
Generating Trees and Proper Riordan Arrays
 Discrete Mathematics
, 2000
"... We use an algebraic approach to study the connection between generating trees and proper Riordan Arrays deriving a theorem that, under suitable conditions, associates a Riordan Array to a generating tree and vice versa. Thus, we can use results from the theory of Riordan Arrays to study properties ..."
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Cited by 17 (8 self)
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in the literature by Chung, Graham, Hoggat and Kleiman in [2] to examine the reduced Baxter permutations. This technique has been successfully applied by West [11, 12] to other classes of permutations and more recently to some other combinatorial classes such as plane trees and lattice paths (see, Barcucci, Del
For most large underdetermined systems of equations, the minimal l1norm nearsolution approximates the sparsest nearsolution
 Comm. Pure Appl. Math
, 2004
"... We consider inexact linear equations y ≈ Φα where y is a given vector in R n, Φ is a given n by m matrix, and we wish to find an α0,ɛ which is sparse and gives an approximate solution, obeying �y − Φα0,ɛ�2 ≤ ɛ. In general this requires combinatorial optimization and so is considered intractable. On ..."
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Cited by 122 (1 self)
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. On the other hand, the ℓ 1 minimization problem min �α�1 subject to �y − Φα�2 ≤ ɛ, is convex, and is considered tractable. We show that for most Φ the solution ˆα1,ɛ = ˆα1,ɛ(y, Φ) of this problem is quite generally a good approximation for ˆα0,ɛ. We suppose that the columns of Φ are normalized to unit ℓ 2 norm
Approximating Oracle Machines for Combinatorial Optimization
, 1994
"... . For every k, an oracle Turing machine M k , and rational polytopes P k (S) for all n and S ` f0; 1g n , are constructed; querying from the set S given as an oracle, M S k solves the separation problem over P k (S) in strongly polynomial time, performing O(n 3k ) arithmetic operations. Each o ..."
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Cited by 1 (0 self)
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for S obtained from P k (S) by applying the conesofmatrices cutting operator of Lov'asz and Schrijver a constant (possibly zero) number of times. Thus, our construction enables a systematic application of the conesofmatrices scheme to any combinatorial optimization problem. Abbreviated title
On the joint path length distribution in random binary trees
 Stud. Appl. Math
"... During the 10th Seminar on Analysis of Algorithms, MSRI, Berkeley, June 2004, Knuth posed the problem of analyzing the left and the right path length in a random binary trees. In particular, Knuth asked about properties of the generating function of the joint distribution of the left and the right p ..."
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Cited by 1 (0 self)
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the first Painlevé transcendent. This is a nonlinear differential equation that has appeared in many modern applications, from nonlinear waves to random matrices. Surprisingly, we find out that the difference between path lengths is of the order n 5/4 where n is the number of nodes in the binary tree
Mortonorder Matrices Deserve Compilers ’ Support
, 1999
"... A proof of concept is offered for the uniform representation of matrices serially in Mortonorder (or Zorder) representation, as well as their divideandconquer processing as quaternary trees. Generally, d dimensional arrays are accessed as 2 dary trees. This data structure is important because, ..."
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A proof of concept is offered for the uniform representation of matrices serially in Mortonorder (or Zorder) representation, as well as their divideandconquer processing as quaternary trees. Generally, d dimensional arrays are accessed as 2 dary trees. This data structure is important because
Using ACO in MOEA/D for Multiobjective Combinatorial Optimization
"... Combining ant colony optimization (ACO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D), this paper proposes a multiobjective evolutionary algorithm, MOEA/DACO. Following other MOEA/Dlike algorithms, MOEA/DACO decomposes an multiobjective optimization problem into a num ..."
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Combining ant colony optimization (ACO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D), this paper proposes a multiobjective evolutionary algorithm, MOEA/DACO. Following other MOEA/Dlike algorithms, MOEA/DACO decomposes an multiobjective optimization problem into a
Multiobjective Combinatorial Optimization by Using Decomposition and Ant Colony
"... Combining ant colony optimization (ACO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D), this paper proposes a multiobjective evolutionary algorithm, MOEA/DACO. Following other MOEA/Dlike algorithms, MOEA/DACO decomposes a multiobjective optimization problem into a numbe ..."
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Combining ant colony optimization (ACO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D), this paper proposes a multiobjective evolutionary algorithm, MOEA/DACO. Following other MOEA/Dlike algorithms, MOEA/DACO decomposes a multiobjective optimization problem into a
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