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A Combinatorial View of the Graph Laplacians
, 2005
"... Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semisupervised learning. Previous research on graph Laplacians investigated their convergence properties to La ..."
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Cited by 3 (1 self)
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known combinatorial NP hard optimization problem. The spectral solutions provide evidence that normalized Laplacian encodes more reasonable considerations for graph partitioning. We also provide some examples to show their differences.
A Combinatorial View of Gene Assembly
, 2004
"... We shall give an introduction to gene assembly based on operations on signed permutations. These operations sort signed permutations to a conjugate of an identity permutation or of its inversion, and they are faithful to the molecular model of gene assembly in ciliates introduced by Ehrenfeucht, Pre ..."
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We shall give an introduction to gene assembly based on operations on signed permutations. These operations sort signed permutations to a conjugate of an identity permutation or of its inversion, and they are faithful to the molecular model of gene assembly in ciliates introduced by Ehrenfeucht, Prescott, and Rozenberg. In particular, the operations on signed permutations are not reductive, that is, the result of an application of an operation corresponds to a full molecule of the molecular model. For the molecular model there are formal reductive models based on strings and graphs.
Broadcasting colourings on trees. A combinatorial view.∗
"... The broadcasting models on a dary tree T arise in many contexts such as discrete mathematics, biology, information theory, statistical physics and computer science. We consider the kcolouring model, i.e. the root of T is assigned an arbitrary colour and, conditional on this assignment, we take a r ..."
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of the tree. However, there is no apparent combinatorial reason why such a result should be true. When k ≥ (1 + )d / ln d, the threshold implies the following: We can couple two broadcasting processes that assign the root different colours such that the probability of having disagreement at the leaves reduces
A geometric and combinatorial view of weighted voting
, 2011
"... ABSTRACT. A natural partial ordering exists on all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper linear games with one generator. We introduce a geometric appr ..."
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Cited by 1 (0 self)
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ABSTRACT. A natural partial ordering exists on all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper linear games with one generator. We introduce a geometric approach to weighted voting by considering the convex polytope of all possible realizations of a weighted game and connect this geometric perspective to the weighted games poset in several ways. In particular, we prove that generic vertical lines in Cn, the union of all weighted nvoter polytopes, correspond to maximal saturated chains in the poset of weighted games, i.e., the poset is a blueprint for how the polytopes fit together to form Cn. Finally, we describe the facets of each polytope, from which we develop a method for determining the weightedness of any linear game that covers or is covered by a weighted game. 1.
Mixing in Time and Space for Lattice Spin Systems: A Combinatorial View
 ALG
, 2004
"... The paper considers spin systems on the ddimensional integer lattice Z^d with nearestneighbor interactions. A sharp equivalence is proved between exponential decay with distance of spin correlations (a spatial property of the equilibrium state) and "superfast" mixing time of the Glaube ..."
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Cited by 29 (7 self)
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The paper considers spin systems on the ddimensional integer lattice Z^d with nearestneighbor interactions. A sharp equivalence is proved between exponential decay with distance of spin correlations (a spatial property of the equilibrium state) and "superfast" mixing time of the Glauber dynamics (a temporal property of a Markov chain Monte Carlo algorithm). While such
Metaheuristics in combinatorial optimization: Overview and conceptual comparison
 ACM COMPUTING SURVEYS
, 2003
"... The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important meta ..."
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Cited by 314 (17 self)
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The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important
NonDeterministic Exponential Time has TwoProver Interactive Protocols
"... We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language ..."
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Cited by 416 (37 self)
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verification scheme for multilinearity of an nvariable function held by an oracle and can be viewed as an independent result on program verification. Its proof rests on combinatorial techniques including the estimation of the expansion rate of a graph.
FUTURE PATHS FOR INTEGER PROGRAMMING AND LINKS TO Artificial Intelligence
, 1986
"... Scope and PurposeA summary is provided of some of the recent (and a few notsorecent) developments that otTer promise for enhancing our ability to solve combinatorial optimization problems. These developments may be usefully viewed as a synthesis of the perspectives of operations research and arti ..."
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Cited by 379 (8 self)
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Scope and PurposeA summary is provided of some of the recent (and a few notsorecent) developments that otTer promise for enhancing our ability to solve combinatorial optimization problems. These developments may be usefully viewed as a synthesis of the perspectives of operations research
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