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On Embedding Ternary Trees into Boolean Hypercubes (Extended Abstract)
"... ) Ajay K. Gupta Hong Wang Department of Computer Science Department of Computer Sciences Western Michigan University Purdue University Kalamazoo, MI 49008 West Lafayette, IN 47907 1 Introduction Given two graphs G and H , an embedding ! f; g ? of G into H is defined by an injective mapping f from ..."
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) Ajay K. Gupta Hong Wang Department of Computer Science Department of Computer Sciences Western Michigan University Purdue University Kalamazoo, MI 49008 West Lafayette, IN 47907 1 Introduction Given two graphs G and H , an embedding ! f; g ? of G into H is defined by an injective mapping f from the nodes of G to the nodes of H together with a mapping g that maps every edge e = (v; w) of G onto a path g(e) connecting f(v) and f(w) in H . We refer to the mapping f as the assignment and for clarity reasons, we refer to the nodes of H as PEs. Three commonly and extensively studied cost measures of an embedding are the dilation, the congestion and the expansion [1, 4, 9, 13, 15, 17]. The dilation ffi is defined as the maximum distance in H between two adjacent nodes in G. The congestion of an edge in H is defined to be the number of paths passing through it, and the maximum congestion of any edge in H is the congestion of the embedding. The expansion ffl is defined to be the ratio o...
Clustering in the Boolean Hypercube in a List Decoding Regime
, 2013
"... We consider the following clustering with outliers problem: Given a set of points X ⊂ {−1, 1}n, such that there is some point z ∈ {−1, 1}n for which Prx∈X [〈x, z 〉 ≥ ε] ≥ δ, find z. We call such a point z a (δ, ε)center of X. In this work we give lower and upper bounds for the task of finding a ( ..."
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We consider the following clustering with outliers problem: Given a set of points X ⊂ {−1, 1}n, such that there is some point z ∈ {−1, 1}n for which Prx∈X [〈x, z 〉 ≥ ε] ≥ δ, find z. We call such a point z a (δ, ε)center of X. In this work we give lower and upper bounds for the task of finding a (δ, ε)center. We first show that for δ = 1−ν close to 1, i.e. in the unique decoding regime, given a (1−ν, ε)centered set our algorithm can find a (1−(1+o(1))ν, (1−o(1))ε)center. More interestingly, we study the list decoding regime, i.e. when δ is close to 0. Our main upper bound shows that for values of ε and δ that are larger than 1/poly log(n), there exists a polynomial time algorithm that finds a (δ − o(1), ε − o(1))center. Moreover, our algorithm outputs a list of centers explaining all of the clusters in the input. Our main lower bound shows that given a set for which there exists a (δ, ε)center, it is hard to find even a (δ/nc, ε)center for some constant c and ε = 1/poly(n), δ = 1/poly(n).
Orthogonal basis for functions over a slice of the Boolean hypercube
, 2014
"... We present a simple, explicit orthogonal basis of eigenvectors for the Johnson and Kneser graphs, based on Young’s orthogonal representation of the symmetric group. Our basis can also be viewed as an orthogonal basis for the vector space of all functions over a slice of the Boolean hypercube (a set ..."
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Cited by 4 (3 self)
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We present a simple, explicit orthogonal basis of eigenvectors for the Johnson and Kneser graphs, based on Young’s orthogonal representation of the symmetric group. Our basis can also be viewed as an orthogonal basis for the vector space of all functions over a slice of the Boolean hypercube (a set
Algorithms for Scalable Synchronization on SharedMemory Multiprocessors
 ACM Transactions on Computer Systems
, 1991
"... Busywait techniques are heavily used for mutual exclusion and barrier synchronization in sharedmemory parallel programs. Unfortunately, typical implementations of busywaiting tend to produce large amounts of memory and interconnect contention, introducing performance bottlenecks that become marke ..."
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Cited by 567 (32 self)
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Busywait techniques are heavily used for mutual exclusion and barrier synchronization in sharedmemory parallel programs. Unfortunately, typical implementations of busywaiting tend to produce large amounts of memory and interconnect contention, introducing performance bottlenecks that become markedly more pronounced as applications scale. We argue that this problem is not fundamental, and that one can in fact construct busywait synchronization algorithms that induce no memory or interconnect contention. The key to these algorithms is for every processor to spin on separate locallyaccessible ag variables, and for some other processor to terminate the spin with a single remote write operation at an appropriate time. Flag variables may be locallyaccessible as a result of coherent caching, or by virtue of allocation in the local portion of physically distributed shared memory. We present a new scalable algorithm for spin locks that generates O(1) remote references per lock acquisition, independent of the number of processors attempting to acquire the lock. Our algorithm provides reasonable latency in the absence of contention, requires only a constant amount of space per lock, and requires no hardware support other than
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.
Probabilistic Boolean networks: a rulebased uncertainty model for gene regulatory networks
, 2002
"... Motivation: Our goal is to construct a model for genetic regulatory networks such that the model class: (i ) incorporates rulebased dependencies between genes; (ii ) allows the systematic study of global network dynamics; (iii ) is able to cope with uncertainty, both in the data and the model selec ..."
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Cited by 382 (58 self)
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Motivation: Our goal is to construct a model for genetic regulatory networks such that the model class: (i ) incorporates rulebased dependencies between genes; (ii ) allows the systematic study of global network dynamics; (iii ) is able to cope with uncertainty, both in the data and the model selection; and (iv ) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes.
The Landscape of Parallel Computing Research: A View from Berkeley
 TECHNICAL REPORT, UC BERKELEY
, 2006
"... ..."
Layout Area of the Hypercube
 Journal of Interconnection Networks
, 2003
"... In this paper we study the square grid area required for laying out H l , the Boolean hypercube of N = 2 vertices. It is shown that this area is ). We describe a layout which occupies this much area and prove that no layout of less area exists. ..."
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Cited by 2 (0 self)
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In this paper we study the square grid area required for laying out H l , the Boolean hypercube of N = 2 vertices. It is shown that this area is ). We describe a layout which occupies this much area and prove that no layout of less area exists.
Distance Browsing in Spatial Databases
, 1999
"... Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is kn ..."
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Cited by 390 (20 self)
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Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is known prior to the invocation of the algorithm. Thus if m#kneighbors are needed, the knearest neighbor algorithm needs to be reinvoked for m neighbors, thereby possibly performing some redundant computations. The second approach is incremental in the sense that having obtained the k nearest neighbors, the k +1 st neighbor can be obtained without having to calculate the k +1nearest neighbors from scratch. The incremental approach finds use when processing complex queries where one of the conditions involves spatial proximity (e.g., the nearest city to Chicago with population greater than a million), in which case a query engine can make use of a pipelined strategy. A general incremental nearest neighbor algorithm is presented that is applicable to a large class of hierarchical spatial data structures. This algorithm is adapted to the Rtree and its performance is compared to an existing knearest neighbor algorithm for Rtrees [45]. Experiments show that the incremental nearest neighbor algorithm significantly outperforms the knearest neighbor algorithm for distance browsing queries in a spatial database that uses the Rtree as a spatial index. Moreover, the incremental nearest neighbor algorithm also usually outperforms the knearest neighbor algorithm when applied to the knearest neighbor problem for the Rtree, although the improvement is not nearly as large as for distance browsing queries. In fact, we prove informally that, at any step in its execution, the incremental...
EFFICIENT EMBEDDINGS OF TREES IN HYPERCUBES*
"... Abstract. The boolean hypercube is a particularly versatile network for parallel computing. It is well known that multidimensional grid machines can be simulated on a hypercube with no communications overhead. In this paper it is shown that every boundeddegree tree can be simulated on the hypercube ..."
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Abstract. The boolean hypercube is a particularly versatile network for parallel computing. It is well known that multidimensional grid machines can be simulated on a hypercube with no communications overhead. In this paper it is shown that every boundeddegree tree can be simulated
Results 1  10
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