Search results for " Computer Science"

showing 10 items of 3983 documents

On the loopless generation of binary tree sequences

1998

Weight sequences were introduced by Pallo in 1986 for coding binary trees and he presented a constant amortized time algorithm for their generation in lexicographic order. A year later, Roelants van Baronaigien and Ruskey developed a recursive constant amortized time algorithm for generating Gray code for binary trees in Pallo's representation. It is common practice to find a loopless generating algorithm for a combinatorial object when enunciating a Gray code for this object. In this paper we regard weight sequences as variations and apply a Williamson algorithm in order to obtain a loopless generating algorithm for the Roelants van Baronaigien and Ruskey's Gray code for weight sequences.

Discrete mathematicsAmortized analysisBinary treeLexicographical orderPseudorandom binary sequenceComputer Science ApplicationsTheoretical Computer ScienceGray codeCombinatoricsSignal ProcessingBinary codeInformation SystemsCoding (social sciences)MathematicsInformation Processing Letters
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Potential approach in marginalizing Gibbs models

1999

Abstract Given an undirected graph G or hypergraph potential H model for a given set of variables V , we introduce two marginalization operators for obtaining the undirected graph G A or hypergraph H A associated with a given subset A ⊂ V such that the marginal distribution of A factorizes according to G A or H A , respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that potential approach allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models. Finally, we explain connections with related works.

Discrete mathematicsApplied MathematicsComparability graphStrength of a graphClique graphlaw.inventionTheoretical Computer ScienceCombinatoricslawGraph powerArtificial IntelligenceGibbs modelLine graphGraph (abstract data type)FactorizationNull graphMarginalizationRandom geometric graphHypergraph modelsSoftwareMathematicsInternational Journal of Approximate Reasoning
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Grundy coloring for power graphs

2003

International audience

Discrete mathematicsApplied Mathematics[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS][ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM][INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS][INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]Power (physics)Brooks' theoremGreedy coloring[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Discrete Mathematics and Combinatorics[ INFO.INFO-DS ] Computer Science [cs]/Data Structures and Algorithms [cs.DS]ComputingMilieux_MISCELLANEOUSMathematics
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Partially Square Graphs, Hamiltonicity and Circumference II

2000

Abstract Given a graph G, its partially square graph G∗ is a graph obtained by adding an edge uv for each pair u, v of vertices of G at distance 2 whenever the vertices u and v have a common neighbor x satisfying the condition NG(x) ⊆ NG[u] ∪ NG[v], where NG[x]= NG(x) ∪ {x}. In case G is a claw-free graph, G∗ is equal to G2, We define σ ∗ t = min{ ∑ x∈ d ∗ G (x): S is an independent set in G ∗ and ∣S∣ = t} , where d ∗ G (x) = ∣{y ∈ V∣ xy ∈ E(G∗)}∣ . We give for hamiltonicity and circumference new sufficient conditions depending on and we improve some known results.

Discrete mathematicsApplied Mathematics[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS][INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS][INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]CircumferenceDistance-regular graphGraphCombinatorics[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Graph powerIndependent setCommon neighborDiscrete Mathematics and CombinatoricsBound graphComputingMilieux_MISCELLANEOUSMathematics
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Forbidden words in symbolic dynamics

2000

AbstractWe introduce an equivalence relation≃between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the≃-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of sofic systems, we prove that the≃-equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having “different slope” are not conjugate.

Discrete mathematicsApplied Mathematicsautomata and formal languages010102 general mathematics[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Symbolic dynamics[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]0102 computer and information sciencesFunction (mathematics)16. Peace & justice01 natural sciencesDecidabilitysymbolic dynamics010201 computation theory & mathematicsEquivalence relationcombinatoric on words0101 mathematicsInvariant (mathematics)Dynamical system (definition)Equivalence (measure theory)Computer Science::Formal Languages and Automata TheoryWord (group theory)ComputingMilieux_MISCELLANEOUSMathematics
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Divisible designs from semifield planes

2002

AbstractWe give a general method to construct divisible designs from semifield planes and we use this technique to construct some divisible designs. In particular, we give the case of twisted field plane as an example.

Discrete mathematicsAutomorphism groupGeneral methodDivisible designsField (mathematics)Division (mathematics)Permutation groupTranslation (geometry)Plane (Unicode)Theoretical Computer ScienceR-permutation groupsCombinatoricsDiscrete Mathematics and CombinatoricsAutomorphism groupsTranslation planesDivision algebrasSemifieldMathematicsDiscrete Mathematics
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Root-restricted Kleenean rotations

2010

We generalize the Kleene theorem to the case where nonassociative products are used. For this purpose, we apply rotations restricted to the root of binary trees.

Discrete mathematicsBinary treeMathematics::Rings and AlgebrasRoot (chord)Kleene theoremComputer Science ApplicationsTheoretical Computer ScienceCombinatoricsMathematics::Group TheoryProduct (mathematics)Signal ProcessingRotation (mathematics)Computer Science::Formal Languages and Automata TheoryInformation SystemsMathematicsInformation Processing Letters
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Generation of Valid Labeled Binary Trees

2003

International audience; Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. Such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.

Discrete mathematicsBinary treeOptimal binary search tree[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Weight-balanced tree[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Scapegoat treeComputer Science::Computational GeometryRandom binary treeCombinatoricsBinary search treeTernary search treeMetric treeMathematicsComputingMethodologies_COMPUTERGRAPHICS
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A bijection between words and multisets of necklaces

2012

Two of the present authors have given in 1993 a bijection Phi between words on a totally ordered alphabet and multisets of primitive necklaces. At the same time and independently, Burrows and Wheeler gave a data compression algorithm which turns out to be a particular case of the inverse of Phi. In the present article, we show that if one replaces in Phi the standard permutation of a word by the co-standard one (reading the word from right to left), then the inverse bijection is computed using the alternate lexicographic order (which is the order of real numbers given by continued fractions) on necklaces, instead of the lexicographic order as for Phi(-1). The image of the new bijection, ins…

Discrete mathematicsBurrows and Wheeler TransformMathematics::CombinatoricsSettore INF/01 - InformaticaFree Lie algebraLie superalgebrastandard permutationLexicographical orderTheoretical Computer ScienceImage (mathematics)CombinatoricsSet (abstract data type)PermutationComputational Theory and MathematicsBijectionDiscrete Mathematics and CombinatoricsGeometry and TopologyComputer Science::Formal Languages and Automata TheoryWord (group theory)MathematicsReal number
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Total and fractional total colourings of circulant graphs

2008

International audience; In this paper, the total chromatic number and the fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional total chromatic number and for 4-regular circulant graphs we find the total chromatic number for some cases and we give the exact value of the fractional total chromatic number in most cases.

Discrete mathematicsCirculant graphMathematics::CombinatoricsFractional total colouring010102 general mathematics[ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM]0102 computer and information sciences[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]01 natural sciencesTotal colouringTheoretical Computer ScienceCombinatoricsMSC 05C15010201 computation theory & mathematicsComputer Science::Discrete MathematicsGraph colouringDiscrete Mathematics and CombinatoricsPhysics::Accelerator PhysicsChromatic scale0101 mathematicsCirculant matrixValue (mathematics)MathematicsDiscrete Mathematics
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