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143
Small and other worlds: Global network structures from local processes
 American Journal of Sociology
, 2005
"... Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributions based on assumptions about simple local social processes. We examine the resulting global structures ..."
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Cited by 39 (2 self)
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Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributions based on assumptions about simple local social processes. We examine the resulting global structures against appropriate Bernoulli graph distributions and provide examples of stochastic global “worlds, ” including small worlds, long path worlds, and nonclustered worlds with many fourcycles. In light of these results we suggest a locally specified social process that produces small world properties. In examining movement from structure to randomness, parameter scaling produces a phase transition at a “temperature ” where regular structures “melt ” into stochastically based counterparts. We provide examples of “frozen ” structures, including “caveman ” graphs, bipartite structures, and cyclic structures.
Topology for distributed inference on graphs
 Jun. 2006 [Online]. Available: http://www.arxiv. org/abs/cs/0606052
"... Abstract—Let decisionmakers collaborate to reach a decision. We consider iterative distributed inference with local intersensor communication, which, under simplifying assumptions, is equivalent to distributed average consensus. We show that, under appropriate conditions, the topology given by the ..."
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Cited by 35 (23 self)
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Abstract—Let decisionmakers collaborate to reach a decision. We consider iterative distributed inference with local intersensor communication, which, under simplifying assumptions, is equivalent to distributed average consensus. We show that, under appropriate conditions, the topology given by the nonbipartite Ramanujan graphs optimizes the convergence rate of this distributed algorithm. Index Terms—Algebraic connectivity, Cayley, consensus algorithm, distributed detection, Laplacian, Ramanujan, random graphs, sensor
Solving Alignment using Elementary Linear Algebra
 IN PROCEEDINGS OF THE 7TH ANNUAL WORKSHOP ON LANAGUAGES AND COMPILERS FOR PARALLEL COMPUTERS
, 1994
"... Data and computation alignment is an important part of compiling sequential programs to architectures with nonuniform memory access times. In this paper, we show that elementary matrix methods can be used to determine communicationfree alignment of code and data. We also solve the problem of repli ..."
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Cited by 32 (5 self)
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Data and computation alignment is an important part of compiling sequential programs to architectures with nonuniform memory access times. In this paper, we show that elementary matrix methods can be used to determine communicationfree alignment of code and data. We also solve the problem of replicating readonly data to eliminate communication. Our matrixbased approach leads to algorithms which are simpler and faster than existing algorithms for the alignment problem. 1 Introduction: A key problem in generating code for nonuniform memory access (NUMA) parallel machines is data and computation placement  that is, determining what work each processor must do, and what data must reside in each local memory. The goal of placement is to exploit parallelism by spreading the work across the processors, and to exploit locality by spreading data so that memory accesses are local whenever possible. The problem of determining a good placement for a program is usually solved in two phases called alignment and distribution.
The Internet Topology Zoo.
 IEEE J. Select. Areas Commun.,
, 2011
"... AbstractThe study of network topology has attracted a great deal of attention in the last decade, but has been hampered by a lack of accurate data. Existing methods for measuring topology have flaws, and arguments about the importance of these have overshadowed the more interesting questions about ..."
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Cited by 29 (6 self)
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AbstractThe study of network topology has attracted a great deal of attention in the last decade, but has been hampered by a lack of accurate data. Existing methods for measuring topology have flaws, and arguments about the importance of these have overshadowed the more interesting questions about network structure. The Internet Topology Zoo is a store of network data created from the information that network operators make public. As such it is the most accurate largescale collection of network topologies available, and includes metadata that couldn't have been measured. With this data we can answer questions about network structure with more certainty than ever before we illustrate its power through a preliminary analysis of the PoPlevel topology of over 140 networks. We find a wide range of network designs not conforming as a whole to any obvious model.
Mobile and Replicated Alignment of Arrays in DataParallel Programs
, 1993
"... When a dataparallel language like Fortran 90 is compiled for a distributedmemory machine, aggregate data objects (such as arrays) are distributed across the processor memories. The mapping determines the amount of residual communication needed to bring operands of parallel operations into alignmen ..."
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Cited by 28 (6 self)
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When a dataparallel language like Fortran 90 is compiled for a distributedmemory machine, aggregate data objects (such as arrays) are distributed across the processor memories. The mapping determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. A common approach is to break the mapping into two stages: first, an alignment that maps all the objects to an abstract template, and then a distribution that maps the template to the processors.
On the Communication Complexity of Randomized Broadcasting in RandomLike Graphs
, 2006
"... Broadcasting algorithms have a various range of applications in different fields of computer science. In this paper we analyze the number of message transmissions generated by efficient randomized broadcasting algorithms in randomlike networks. We mainly consider the classical random graph model, i ..."
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Cited by 24 (3 self)
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Broadcasting algorithms have a various range of applications in different fields of computer science. In this paper we analyze the number of message transmissions generated by efficient randomized broadcasting algorithms in randomlike networks. We mainly consider the classical random graph model, i.e., a graph Gp with n nodes in which any two arbitrary nodes are connected with probability p, independently. For these graphs, we present an efficient broadcasting algorithm based on the random phone call model introduced by Karp et al. [21], and show that the total number of message transmissions generated by this algorithm is bounded by an asymptotically optimal value in almost all connected random graphs. More precisely, we show that if p ≥ log δ n/n for some constant δ> 2, then we are able to broadcast any information r in a random graph Gp of size n in O(log n) steps by using at most O(n max{log log n, log n / log d}) transmissions related to r, where d = pn denotes the expected average degree in Gp. We also show that for these kind of graphs there is a a matching lower bound on the number of transmissions generated by any efficient broadcasting algorithm which works within the limits of the random phone call model. Please note that the main result holds with probability 1 − 1/n Ω(1) , even if n and d are unknown to the nodes of the graph. The algorithm we present in this paper is based on a simple communication model [21], is scalable, and robust. It can efficiently handle restricted communication failures and certain changes in the size of the network, and can also be extended to certain types of truncated power law graphs based on the models of [1, 2, 5]. In addition, our methods and results might be useful for further research on this field.
A partitioning advisory system for networked dataparallel processing
 Concurrency: Practice and Experience
, 1995
"... With the increased performance capabilities of desktop computers, networked computing has become a popular vehicle for using parallelism to solve a variety of computationally intense problems. However, node heterogeneity and high communication costs may limit performance unless the problem space is ..."
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Cited by 21 (1 self)
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With the increased performance capabilities of desktop computers, networked computing has become a popular vehicle for using parallelism to solve a variety of computationally intense problems. However, node heterogeneity and high communication costs may limit performance unless the problem space is carefully partitioned across the network in a way that considers both the capabilities of the machines and the high network communication costs. We describe an advisory system that is designed to help the programmer, compiler, or runtime environment choose the best decomposition strategy for partitioning specific dataparallel applications across a given collection of machines. The system includes provisions for assessing the capabilities of the participating machines and the network in light of the current workload. Given information about the problem space, the machine speeds, and the network, the system provides a ranking of three standard partitioning methods. We test the validity of our system by comparing the observed relative performance with predicted relative performance of different data decompositions on a program with a variable number of floating point operations and a 5point stencil communication pattern.
CONTEST: A controllable test matrix toolbox for MATLAB
 ACM Trans. Math. Software
, 2008
"... Networks describing connectivity structures arise across a vast range of application areas. Examples where it has proved useful to record data include interactions between genes [Kauffman 1969], proteins [de Silva and Stumpf 2005], cortical regions [Kamper et al. 2002; Sporns and Zwi 2004], internet ..."
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Cited by 17 (2 self)
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Networks describing connectivity structures arise across a vast range of application areas. Examples where it has proved useful to record data include interactions between genes [Kauffman 1969], proteins [de Silva and Stumpf 2005], cortical regions [Kamper et al. 2002; Sporns and Zwi 2004], internet nodes [Faloutsos et al. 1999], web pages [Broder et al. 2000; Page et al. 1998], countries [Fagiolo 2007], coauthors [Newman 2004], telephones [Abello et al. 1998], assets on the stock market [Boginski
A Quantitative Comparison of StressMinimization Approaches for Offline Dynamic Graph Drawing
, 2012
"... In dynamic graph drawing, the input is a sequence of graphs for which a sequence of layouts is to be generated such that the quality of individual layouts is balanced with layout stability over time. Qualitatively different extensions of drawing algorithms for static graphs to the dynamic case have ..."
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Cited by 15 (2 self)
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In dynamic graph drawing, the input is a sequence of graphs for which a sequence of layouts is to be generated such that the quality of individual layouts is balanced with layout stability over time. Qualitatively different extensions of drawing algorithms for static graphs to the dynamic case have been proposed, but little is known about their relative utility. We report on a quantitative study comparing the three prototypical extensions via their adaptation for the stressminimization framework. While some findings are more subtle, the linking approach connecting consecutive instances of the same vertex is found to be the overall method of choice.
Isomorphism and Embedding Problems for Infinite Limits of ScaleFree Graphs
"... The study of random graphs has traditionally been dominated by the closelyrelated models G(n, m), in which a graph is sampled from the uniform distribution on graphs with n vertices and m edges, and with probability p. Recently, however, there has been considerable interest in alternate rand ..."
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Cited by 14 (0 self)
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The study of random graphs has traditionally been dominated by the closelyrelated models G(n, m), in which a graph is sampled from the uniform distribution on graphs with n vertices and m edges, and with probability p. Recently, however, there has been considerable interest in alternate random graph models designed to more closely approximate the properties of complex realworld networks such as the Web graph, the Internet, and large social networks. Two of the most wellstudied of these are the closely related "preferential attachment" and "copying" models, in which vertices arrive onebyone in sequence and attach at random in "richgetricher" fashion to d earlier vertices. Here we study