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130
Exploiting the Block Structure of the Web for Computing PageRank
, 2003
"... The web link graph has a nested block structure: the vast majority of hyperlinks link pages on a host to other pages on the same host, and many of those that do not link pages within the same domain. We show how to exploit this structure to speed up the computation of PageRank by a 3stage alg ..."
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Cited by 157 (4 self)
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The web link graph has a nested block structure: the vast majority of hyperlinks link pages on a host to other pages on the same host, and many of those that do not link pages within the same domain. We show how to exploit this structure to speed up the computation of PageRank by a 3stage algorithm whereby (1) the local PageRanks of pages for each host are computed independently using the link structure of that host, (2) these local PageRanks are then weighted by the "importance" of the corresponding host, and (3) the standard PageRank algorithm is then run using as its starting vector the weighted concatenation of the local PageRanks. Empirically, this algorithm speeds up the computation of PageRank by a factor of 2 in realistic scenarios. Further, we develop a variant of this algorithm that efficiently computes many different "personalized" PageRanks, and a variant that efficiently recomputes PageRank after node updates.
A Decomposition Approach for Stochastic Reward Net Models
 Perf. Eval
, 1993
"... We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of nearindependence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel ..."
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Cited by 126 (32 self)
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We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of nearindependence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel and an arc from submodel A to submodel B corresponds to a parameter value that B must receive from A. The quantities exchanged between submodels are based on only three primitives. The import graph normally contains cycles, so the solution method is based on fixed point iteration. Any SRN containing one or more of the nearlyindependent structures we present, commonly encountered in practice, can be analyzed using our approach. No other restriction on the SRN is required. We apply our technique to the analysis of a flexible manufacturing system.
Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems
 SIAM Rev
, 1989
"... Abstract. A concept called stochastic complementation is an idea which occurs naturally, although not always explicitly, in the theory and application of finite Markov chains. This paper brings this idea to the forefront with an explicit definition and a development of some of its properties. Applic ..."
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Cited by 97 (7 self)
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Abstract. A concept called stochastic complementation is an idea which occurs naturally, although not always explicitly, in the theory and application of finite Markov chains. This paper brings this idea to the forefront with an explicit definition and a development of some of its properties. Applications of stochastic complementation are explored with respect to problems involving uncoupling procedures in the theory of Markov chains. Furthermore, the role of stochastic complementation in the development of the classical Simon–Ando theory of nearly reducible system is presented. Key words. Markov chains, stationary distributions, stochastic matrix, stochastic complementation, nearly reducible systems, Simon–Ando theory
Markovian Analysis of Large Finite State Machines
 IEEE Transactions on CAD
, 1996
"... Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. In this paper we present symbolic algorithms to compute the steadystate probabilities for very large finite state machines (up to 10 ..."
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Cited by 76 (7 self)
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Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. In this paper we present symbolic algorithms to compute the steadystate probabilities for very large finite state machines (up to 10 27 states). These algorithms, based on Algebraic Decision Diagrams (ADDs)  an extension of BDDs that allows arbitrary values to be associated with the terminal nodes of the diagrams  determine the steadystate probabilities by regarding finite state machines as homogeneous, discreteparameter Markov chains with finite state spaces, and by solving the corresponding ChapmanKolmogorov equations. We first consider finite state machines with state graphs composed of a single terminal strongly connected component; for this type of systems we have implemented two solution techniques: One is based on the GaussJacobi iteration, the other one is based on simple matrix multiplication. Then we...
Resource Sharing for BookAhead and InstantaneousRequest Calls
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1999
"... In order to provide an adequate quality of service to largebandwidth calls, such as video conference calls, service providers of integrated services networks may want to allow some customers to book their calls ahead, i.e., make advance reservations. We propose a scheme for sharing resources among ..."
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Cited by 71 (10 self)
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In order to provide an adequate quality of service to largebandwidth calls, such as video conference calls, service providers of integrated services networks may want to allow some customers to book their calls ahead, i.e., make advance reservations. We propose a scheme for sharing resources among bookahead (BA) calls (that announce their call holding times as well as their call initiation times upon arrival) and nonBA calls (that do not announce their holding times). It is possible to share resources without allowing any calls in progress to be interrupted, but in order to achieve a more efficient use of resources, we think that it may be desirable to occasionally allow a call in progress to be interrupted. (In practice, it may be possible to substitute service degradation, such as bit dropping or coarser encoding of video, for interruption.) Thus, we propose an admission control algorithm in which a call is admitted if an approximate interrupt probability (computed in real time) i...
Numerical Methods in Markov Chain Modelling
 Operations Research
, 1996
"... This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solvi ..."
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Cited by 36 (8 self)
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This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous, singular linear system. We present several methods based on combinations of Krylov subspace techniques, single vector power iteration/relaxation procedures and acceleration techniques. We compare the performance of these methods on some realistic problems. Key words: Markov chain models; Homogeneous linear systems; Direct methods; Successive Overrelaxation; Preconditioned power iterations; Arnoldi's method; GMRES. y IRISA, Rennes, France. Research supported by CNRS (87:N 920070). Research Institute for Advanced Computer Science, NASA Ames Research Center. Moffett Field CA 94035. Research supported by Cooperative Agreement NCC 2387 between the National Aeronautics and S...
Probabilistic Analysis of Large Finite State
 Machines”, Proceedings of the 31st Design Automation Conference
, 1994
"... Regarding nite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal veri cation problems. Recently, we have shown how symbolic algorithms based onAlgebraic Decision Diagrams may be used tocalculate the steadystate probabilities ..."
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Cited by 34 (1 self)
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Regarding nite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal veri cation problems. Recently, we have shown how symbolic algorithms based onAlgebraic Decision Diagrams may be used tocalculate the steadystate probabilities of nite state machines with more than 10 8 states. These algorithms treated machines with state graphs composed of a single terminal strongly connected component. In this paper we consider the most general case of systems which can be modeled as state machines with arbitrary transition structures. The proposed approach exploits structural information to decompose and simplify the state graph of the machine. 1
A Simple Time Scale Decomposition Technique for Stochastic Process Algebras
 The Computer Journal
, 1995
"... this paper we present cases when this structure may be used to inform the solution of the model, leading to an efficient solution based on a decomposition of the underlying Markov process. The decomposition which we consider is time scale decomposition, based on Courtois's ..."
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Cited by 32 (20 self)
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this paper we present cases when this structure may be used to inform the solution of the model, leading to an efficient solution based on a decomposition of the underlying Markov process. The decomposition which we consider is time scale decomposition, based on Courtois's
Numerical Experiments with Iteration and Aggregation for Markov Chains
 ORSA Journal on Computing
, 1996
"... This paper describes an iterative aggregation/disaggregation method for computing the stationary probability vector of a nearly completely decomposable Markov chain. The emphasis is on the implementation of the algorithm and on the results that are obtained when it is applied to three modelling exam ..."
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Cited by 31 (9 self)
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This paper describes an iterative aggregation/disaggregation method for computing the stationary probability vector of a nearly completely decomposable Markov chain. The emphasis is on the implementation of the algorithm and on the results that are obtained when it is applied to three modelling examples that have been used in the analysis of computer/communication systems. Where applicable, a comparison with standard iterative and direct methods for solving the same problems, is made. Key words: Large Markov Chain Models; NearCompleteDecomposability; Iteration and Aggregation; Numerical Experiments. Research supported in part by NSF (DDM8906248) Introduction Let Q be the infinitesimal generator of an irreducible continuoustime Markov chain and let ß be its stationary probability vector. Thus q ij denotes the rate of transition from state i to state j; q ii = \Gamma P j 6=i q ij and ß i is the probability that the system is in state i at statistical equilibrium. It may be sho...