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Rainbow copies of C4 in edgecolored hypercubes
, 2013
"... For positive integers k and d such that 4 ≤ k < d and k 6 = 5, we determine the maximum number of rainbow colored copies of C4 in a kedgecoloring of the ddimensional hypercube Qd. Interestingly, the kedgecolorings of Qd yielding the maximum number of rainbow copies of C4 also have the prop ..."
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For positive integers k and d such that 4 ≤ k < d and k 6 = 5, we determine the maximum number of rainbow colored copies of C4 in a kedgecoloring of the ddimensional hypercube Qd. Interestingly, the kedgecolorings of Qd yielding the maximum number of rainbow copies of C4 also have
Rainbow edgecoloring and rainbow domination
, 2012
"... Let G be an edgecolored graph with n vertices. A rainbow subgraph is a subgraph whose edges have distinct colors. The rainbow edgechromatic number of G, written ˆχ ′(G), is the minimum number of rainbow matchings needed to cover E(G). An edgecolored graph is ttolerant if it contains no monochroma ..."
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Cited by 2 (2 self)
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Let G be an edgecolored graph with n vertices. A rainbow subgraph is a subgraph whose edges have distinct colors. The rainbow edgechromatic number of G, written ˆχ ′(G), is the minimum number of rainbow matchings needed to cover E(G). An edgecolored graph is ttolerant if it contains
Edgecolorings avoiding rainbow and monochromatic subgraphs
 Discrete Math
"... For two graphs G and H, let the mixed antiRamsey numbers, maxR(n; G, H), (minR(n; G, H)) be the maximum (minimum) number of colors used in an edgecoloring of a complete graph with n vertices having no monochromatic subgraph isomorphic to G and no totally multicolored (rainbow) subgraph isomorphic ..."
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Cited by 8 (2 self)
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For two graphs G and H, let the mixed antiRamsey numbers, maxR(n; G, H), (minR(n; G, H)) be the maximum (minimum) number of colors used in an edgecoloring of a complete graph with n vertices having no monochromatic subgraph isomorphic to G and no totally multicolored (rainbow) subgraph isomorphic
Rainbows in the hypercube
, 2004
"... Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary ntuples and two vertices are adjacent iff the corresponding ntuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G, H) be the largest ..."
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Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary ntuples and two vertices are adjacent iff the corresponding ntuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G, H) be the largest
Implementing data cubes efficiently
 In SIGMOD
, 1996
"... Decision support applications involve complex queries on very large databases. Since response times should be small, query optimization is critical. Users typically view the data as multidimensional data cubes. Each cell of the data cube is a view consisting of an aggregation of interest, like total ..."
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Cited by 545 (1 self)
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to materialize. The greedy algorithm performs within a small constant factor of optimal under a variety of models. We then consider the most common case of the hypercube lattice and examine the choice of materialized views for hypercubes in detail, giving some good tradeoffs between the space used
Pastry: Scalable, distributed object location and routing for largescale peertopeer systems
, 2001
"... This paper presents the design and evaluation of Pastry, a scalable, distributed object location and routing scheme for widearea peertopeer applications. Pastry provides applicationlevel routing and object location in a potentially very large overlay network of nodes connected via the Internet. ..."
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Cited by 2063 (50 self)
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. It can be used to support a wide range of peertopeer applications like global data storage, global data sharing, and naming. An insert operation in Pastry stores an object at a userdefined number of diverse nodes within the Pastry network. A lookup operation reliably retrieves a copy of the requested
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
Fast Parallel Algorithms for ShortRange Molecular Dynamics
 JOURNAL OF COMPUTATIONAL PHYSICS
, 1995
"... Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of interatomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dyn ..."
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Cited by 622 (6 self)
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. The algorithms are tested on a standard LennardJones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers  the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray YMP and C90 algorithm shows
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
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