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711
A Faster Algorithm for Betweenness Centrality
 Journal of Mathematical Sociology
, 2001
"... The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require #(n ) time and #(n ) space, where n is the number of actors in the network. ..."
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Cited by 554 (5 self)
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The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require #(n ) time and #(n ) space, where n is the number of actors in the network.
Pregel: A system for largescale graph processing
 IN SIGMOD
, 2010
"... Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model ..."
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Cited by 496 (0 self)
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Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertexcentric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and faulttolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distributionrelated details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.
An open graph visualization system and its applications to software engineering
 SOFTWARE  PRACTICE AND EXPERIENCE
, 2000
"... We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, highquality static and dynamic layout alg ..."
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Cited by 453 (9 self)
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We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, highquality static and dynamic layout algorithms, and the ability to handle sizable graphs. We conclude with a description of the applications of this package to a variety of software engineering tools.
Realtime motion planning for agile autonomous vehicles,
 AIAA Journal of Guidance and Control
, 2002
"... Planning the path of an autonomous,agile vehicle in a dynamicenvironment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities. Recent efforts aimed at using randomized algorithms for planning the path of kinematic and dynamic vehicles have demo ..."
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Cited by 225 (16 self)
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Planning the path of an autonomous,agile vehicle in a dynamicenvironment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities. Recent efforts aimed at using randomized algorithms for planning the path of kinematic and dynamic vehicles have demonstrated considerable potential for implementation on future autonomous platforms. This paper builds upon these efforts by proposing a randomized path planning architecture for dynamical systems in the presence of xed and moving obstacles. This architecture addresses the dynamic constraints on the vehicle's motion, and it provides at the same time a consistent decoupling between lowlevel control and motion planning. The path planning algorithm retains the convergence properties of its kinematic counterparts. System safety is also addressed in the face of nite computation times by analyzing the behavior of the algorithm when the available onboard computation resources are limited, and the planning must be performed in real time. The proposed algorithm can be applied to vehicles whose dynamics are described either by ordinary differential equations or by higherlevel, hybrid representations. Simulation examples involving a ground robot and a small autonomous helicopter are presented and discussed.
The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes
 Mol. Biol. Evol
, 2001
"... SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for pap ..."
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Cited by 191 (7 self)
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SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTE 1The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes.
Approximate Reachability Analysis of PiecewiseLinear Dynamical Systems
, 2000
"... . In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much small ..."
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Cited by 140 (31 self)
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. In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much smaller than in previouslyused methods. The d=dt system can, so far, treat nontrivial continuous systems, hybrid systems, convex differential inclusions and controller synthesis problems. 1 Introduction The problem of calculating reachable states for continuous and hybrid systems has emerged as one of the major problems in hybrid systems research [G96,GM98,DM98,KV97,V98,GM99,CK99,PSK99,HHMW99]. It constitutes a prerequisite for exporting algorithmic verification methodology outside discrete systems or hybrid systems with piecewisetrivial dynamics. For computer scientists it poses new challenges in treating continuous functions and their approximations and in applying computational geometry...
How the global structure of protein interaction networks evolves,”
 Proceedings of the Royal Society B,
, 2003
"... Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genom ..."
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Cited by 105 (2 self)
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Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genome data and are sufficiently high to affect network structure on short timescales. For instance, more than 100 interactions may be added to the yeast network every million years, a fraction of which adds previously unconnected proteins to the network. Highly connected proteins show a greater rate of interaction turnover than proteins with few interactions. From these observations one can explain (without natural selection on global network structure) the evolutionary sustenance of the most prominent network feature, the distribution of the frequency P(d ) of proteins with d neighbours, which is broadtailed and consistent with a power law, that is: P(d )~d 2g .
Robust Geometric Computation
, 1997
"... Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section... ..."
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Cited by 80 (14 self)
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Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section...