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Using DNA to Solve the Minimal Vertex Covering Problem
"... Abstract. Plasmid DNA algorithm of the minimal vertex covering problem is proposed upon the basic idea and operation of plasmid DNA computing model. In the plasmid DNA algorithm, though an appropriate encoding and the basic biological operation, we finish the generation and separation of solution. O ..."
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Abstract. Plasmid DNA algorithm of the minimal vertex covering problem is proposed upon the basic idea and operation of plasmid DNA computing model. In the plasmid DNA algorithm, though an appropriate encoding and the basic biological operation, we finish the generation and separation of solution
A GA based Approach to Find Minimal Vertex Cover
"... Genetic Algorithms are a class of Optimization Techniques which has been developed under inspiration of the Darwinian Theory of Survival of the Fittest. This technique has been successfully used to solve many optimization problems which otherwise pose huge challenges for computation. This paper pres ..."
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presents a GA based approach to solve the Minimal Vertex Cover problem of Graph Theory.
ON THE SIZE OF A MINIMAL VERTEX COVER IN A RANDOM SUBGRAPH OF THE nCUBE
"... We describe and analyze a construction of a vertex cover (consisting of subcubes) in a random subgraph of the ncube. The main idea of the construction is to select subcubes with minimal intersection into the vertex cover. We estimate the upper bound of such a vertex cover. Our analysis gives a theo ..."
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We describe and analyze a construction of a vertex cover (consisting of subcubes) in a random subgraph of the ncube. The main idea of the construction is to select subcubes with minimal intersection into the vertex cover. We estimate the upper bound of such a vertex cover. Our analysis gives a
Generation of minimal vertex covers for row/column allocation in selfrepairable arrays
 IEEE Transactions on Computers
, 1996
"... AbsfracfThis paper lays foundations for an approach to onchip row/column allocation that exploits certain properties offered by laterally connected networks of simple threshold devices. As a sample application, it is demonstrated how electronic implementations of these networks can be used as the ..."
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Cited by 5 (0 self)
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as the basis for effective memory array repair systems that require little hardware overhead. Index TermsSelfrepair, redundant memory, embedded memory, neural network, vertex cover problem. 1
Parameterized Algorithms for Double Hypergraph Dualization with Rank Limitation and Maximum Minimal Vertex Cover
"... Motivated by the need for succinct representations of all “small” transversals (or hitting sets) of a hypergraph of fixed rank, we study the complexity of computing such a representation. Next, the existence of a minimal hitting set of at least a given size arises as a subproblem. We give one algori ..."
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algorithm for hypergraphs of any fixed rank, and we largely improve an earlier algorithm (by H. Fernau, 2005) for the rank2 case, i.e., for computing a minimal vertex cover of at least a given size in a graph. We were led to these questions by combinatorial aspects of the protein inference problem
Minimal vertex covers on finiteconnectivity random graphs  a hardsphere latticegas picture
, 2008
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A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
Convergent Treereweighted Message Passing for Energy Minimization
 ACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI), 2006. ABSTRACTACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI)
, 2006
"... Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy ..."
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Cited by 491 (16 self)
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Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound
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