Search results for "Application"

showing 10 items of 5559 documents

The Rotation χ-Lattice of Ternary Trees

2001

This paper generalizes to k-ary trees the well-known rotation transformation on binary trees. For brevity, only the ternary case is developped. The rotation on ternary trees is characterized using some codings of trees. Although the corresponding poset is not a lattice, we show that it is a χ-lattice in the sense of Leutola–Nieminen. Efficient algorithms are exhibited to compute meets and joins choosen in a particular way.

Discrete mathematicsNumerical AnalysisBinary treeTernary treeWeight-balanced treeComputer Science ApplicationsTheoretical Computer ScienceCombinatoricsComputational MathematicsComputational Theory and MathematicsTernary search treeTernary operationTamari latticePartially ordered setRotation (mathematics)SoftwareMathematicsComputing
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Error analysis for a special X-spline

1979

Clenshaw and Negus [1] defined the cubic X-spline, and they applied it to an interpolation problem. In the present paper, for the same interpolation problem, an interpolating splinew is considered by combining two specialX-splines. The construction ofw is such that the computational labour for its determination, in the case of piecewise equally spaced knots, is less than that of the conventional cubic splines c . A complete error analysis ofw is done. One of the main results is that, in the case of piecewise equally spaced knots,w ands c have essentially the same error estimates.

Discrete mathematicsNumerical AnalysisMathematics::Numerical AnalysisComputer Science ApplicationsTheoretical Computer ScienceComputational MathematicsSpline (mathematics)Computational Theory and MathematicsError analysisPiecewiseApplied mathematicsMathematical Physics and MathematicsComputer communication networksSoftwareMathematicsInterpolationComputing
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The Monadic Quantifier Alternation Hierarchy over Grids and Graphs

2002

AbstractThe monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k+1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k+1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrar…

Discrete mathematicsPolynomial hierarchyDirected graphMonadic predicate calculusAutomatonTheoretical Computer ScienceComputer Science ApplicationsCombinatoricsTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESComputational Theory and MathematicsAnalytical hierarchyComplexity classAutomata theoryGraph propertyMathematicsInformation SystemsInformation and Computation
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On the size of transducers for bidirectional decoding of prefix codes

2012

In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [ IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X . We find some bounds of such a number of states in relation wi…

Discrete mathematicsPrefix codeBlock codeSettore INF/01 - InformaticaGeneral MathematicsConcatenated error correction codeprefix codeList decodingSerial concatenated convolutional codesSequential decodingLinear codeComputer Science ApplicationsPrefixbilateral decodingVariable length codetransducersAlgorithmComputer Science::Formal Languages and Automata TheorySoftwareMathematics
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Loop-free Gray code algorithm for the e-restricted growth functions

2011

The subject of Gray codes algorithms for the set partitions of {1,2,...,n} had been covered in several works. The first Gray code for that set was introduced by Knuth (1975) [5], later, Ruskey presented a modified version of [email protected]?s algorithm with distance two, Ehrlich (1973) [3] introduced a loop-free algorithm for the set of partitions of {1,2,...,n}, Ruskey and Savage (1994) [9] generalized [email protected]?s results and give two Gray codes for the set of partitions of {1,2,...,n}, and recently, Mansour et al. (2008) [7] gave another Gray code and loop-free generating algorithm for that set by adopting plane tree techniques. In this paper, we introduce the set of e-restricte…

Discrete mathematicsPrefix codeGeneralizationOrder (ring theory)Computer Science ApplicationsTheoretical Computer ScienceCombinatoricsSet (abstract data type)Gray codeTree (descriptive set theory)Signal ProcessingFunction representationRepresentation (mathematics)AlgorithmInformation SystemsMathematicsInformation Processing Letters
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An exact and efficient approach for computing a cell in an arrangement of quadrics

2006

AbstractWe present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected plana…

Discrete mathematicsPure mathematicsArrangementsControl and OptimizationFunction field of an algebraic varietyAlgebraic curvesMathematicsofComputing_NUMERICALANALYSISComputational geometryComputer Science ApplicationsComputational MathematicsComputational Theory and MathematicsJacobian curveAlgebraic surfaceComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONReal algebraic geometryAlgebraic surfacesExact algebraic computationAlgebraic functionGeometry and TopologyAlgebraic curveAlgebraic numberRobustnessMathematicsSingular point of an algebraic varietyComputational Geometry
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On approximate-type systems generated by L-relations

2014

The aim of this work is to study approximate-type systems induced by L-relations in the framework of the general theory of M-approximate systems introduced in [42] and its generalizations. Special attention is payed to the structural properties of lattices of such systems and to the study of connections between categories of such systems and the corresponding categories of sets endowed with L-relations.

Discrete mathematicsPure mathematicsInformation Systems and ManagementGeneral theoryArtificial IntelligenceControl and Systems EngineeringLattice (order)SemilatticeSoftwareComputer Science ApplicationsTheoretical Computer ScienceMathematicsInformation Sciences
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An Exact Algorithm for the Quadratic Assignment Problem on a Tree

1989

The Tree QAP is a special case of the Quadratic Assignment Problem (QAP) where the nonzero flows form a tree. No condition is required for the distance matrix. This problem is NP-complete and is also a generalization of the Traveling Salesman Problem. In this paper, we present a branch-and-bound algorithm for the exact solution of the Tree QAP based on an integer programming formulation of the problem. The bounds are computed using a Lagrangian relaxation of this formulation. To solve the relaxed problem, we present a Dynamic Programming algorithm which is polynomially bounded. The obtained lower bound is very sharp and equals the optimum in many cases. This fact allows us to employ a redu…

Discrete mathematicsQuadratic assignment problemManagement Science and Operations ResearchTravelling salesman problemComputer Science ApplicationsReduction (complexity)Tree (data structure)symbols.namesakeExact algorithmLagrangian relaxationsymbolsInteger programmingGeneralized assignment problemMathematicsOperations Research
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A simple algorithm for generating neuronal dendritic trees

1990

Abstract A simple, efficient algorithm is presented for generating the codewords of all neuronal dendritic trees with a given number of terminal nodes. Furthermore, a procedure is developed for deciding if different codewords correspond to topologically equivalent trees.

Discrete mathematicsQuantitative Biology::Neurons and CognitionEfficient algorithmHealth InformaticsDendritesData_CODINGANDINFORMATIONTHEORYData structureModels BiologicalComputer Science ApplicationsTerminal (electronics)Simple (abstract algebra)Computer SimulationTopological conjugacyMathematical ComputingAlgorithmAlgorithmsSoftwareSIMPLE algorithmComputer Science::Information TheoryMathematicsComputer Methods and Programs in Biomedicine
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A general metric regularity in asplund banach spaces

1998

This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space.

Discrete mathematicsRange (mathematics)Control and OptimizationSimple (abstract algebra)Signal ProcessingMetric (mathematics)Banach spaceSpace (mathematics)AnalysisComputer Science ApplicationsMathematicsNumerical Functional Analysis and Optimization
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