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122
The structure and function of complex networks
 SIAM REVIEW
, 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
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Cited by 1415 (9 self)
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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
How to Model an Internetwork
 In Proceedings of IEEE INFOCOM
, 1996
"... Graphs are commonly used to model the structure of internetworks, for the study of problems ranging from routing to resource reservation. A variety of graph models are found in the literature, including regular topologies such as rings or stars, "wellknown" topologies such as the original ARPAnet, ..."
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Cited by 682 (8 self)
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Graphs are commonly used to model the structure of internetworks, for the study of problems ranging from routing to resource reservation. A variety of graph models are found in the literature, including regular topologies such as rings or stars, "wellknown" topologies such as the original ARPAnet, and randomly generated topologies. Less common is any discussion of how closely these models correlate with real network topologies. We consider the problem of efficiently generating graph models that accurately reflect the topological properties of real internetworks. We compare properties of graphs generated using various methods with those of real internets. We also propose efficient methods for generating topologies with particular properties, including a TransitStub model that correlates well with Internet structure. Improved models for internetwork structure have the potential to impact the significance of simulation studies of internetworking solutions, providing basis for the validi...
Modeling Internet Topology
 IEEE Communications Magazine
, 1997
"... The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graphbased ..."
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Cited by 417 (20 self)
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The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graphbased models can be used to represent the topology of large networks, particularly aspects of locality and hierarchy present in the Internet. Two implementations that generate networks whose topology resembles that of typical internetworks are described, together with publicly available source code. 1 Introduction The explosive growth of networking, and particularly of the Internet, has been accompanied by a wide range of internetworking problems related to routing, resource reservation, and administration. The study of algorithms and policies to address such problems often involves simulation or analysis using an abstraction or model of the actual network structure. The reason for this is clear:...
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
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Cited by 322 (79 self)
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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunctionfree) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the stateoftheart implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, functionfree disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of
A quantitative comparison of graphbased models for internet topology
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and randomly ..."
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Cited by 222 (3 self)
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Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and randomly generated topologies. While many researchers rely upon graphs for analytic and simulation studies, there has been little analysis of the implications of using a particular model, or how the graph generation method may a ect the results of such studies. Further, the selection of one generation method over another is often arbitrary, since the differences and similarities between methods are not well understood. This paper considers the problem of generating and selecting graph models that reflect the properties of real internetworks. We review generation methods in common use, and also propose several new methods. We consider a set of metrics that characterize the graphs produced by a method, and we quantify similarities and differences amongst several generation methods with respect to these metrics. We also consider the effect of the graph model in the context of a speciffic problem, namely multicast routing.
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 185 (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.
GRASP and path relinking for 2layer straight line crossing minimization
 INFORMS Journal on Computing
, 1999
"... ABSTRACT — In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the problem of minimizing straightline crossings in a 2layer graph. The procedure is fast and is particularly appealing when dealing with lowdensity graphs. When a modest increase in computational time ..."
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Cited by 87 (15 self)
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ABSTRACT — In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the problem of minimizing straightline crossings in a 2layer graph. The procedure is fast and is particularly appealing when dealing with lowdensity graphs. When a modest increase in computational time is allowed, the procedure may be coupled with a path relinking strategy to search for improved outcomes. Although the principles of path relinking have appeared in the tabu search literature, this search strategy has not been fully implemented and tested. We perform extensive computational experiments with more than 3,000 graph instances to first study the effect of changes in critical search parameters and then to compare the efficiency of alternative solution procedures. Our results indicate that graph density is a major influential factor on the performance of a solution procedure. Laguna and Martí / 2 The problem of minimizing straightline crossings in layered graphs has been the subject of study for at least 17 years, beginning with the Relative Degree Algorithm introduced by Carpano [2]. The problem consists of aligning the two shores V1 and V2 of a bipartite graph G = (V1, V2, E) on two parallel straight lines (layers) such that the number of crossing between the edges in E is minimized
Default Reasoning System DeReS
, 1996
"... In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, finding one or all extensions (if at least one exists) and querying if a formula belongs to one ..."
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Cited by 71 (5 self)
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In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, finding one or all extensions (if at least one exists) and querying if a formula belongs to one or all extensions. If an input theory is a logic program, DeReS computes stable models of this program and supports queries on membership of an atom in some or all stable models. The paper contains an account of our preliminary experiments with DeReS and a discussion of the results. We show that a choice of a propositional prover is critical for the efficiency of DeReS. We also present a general technique that eliminates the need for some global consistency checks and results in substantial speedups. We experimentally demonstrate the potential of the concept of relaxed stratification for making automated reasoning systems practical. 1 INTRODUCTION The area of nonmonotonic l...
Fast Estimation of Diameter and Shortest Paths (without Matrix Multiplication)
, 1996
"... this paper is organized as follows. We begin by presenting some definitions and useful observations in Section 2. In Section 3, we describe the algorithms for distinguishing between graphs of diameter 2 and 4, and the extension to obtaining a ratio 2=3 approximation to the diameter. Then, in Section ..."
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Cited by 67 (2 self)
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this paper is organized as follows. We begin by presenting some definitions and useful observations in Section 2. In Section 3, we describe the algorithms for distinguishing between graphs of diameter 2 and 4, and the extension to obtaining a ratio 2=3 approximation to the diameter. Then, in Section 4, we apply the ideas developed in estimating the diameter to obtain the promised algorithm for an additive approximation for APSP. Finally, in Section 5 we present an empirical study of the performance of our algorithm for allpairs shortest paths.
2Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms
, 1997
"... We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NPhard, and that for the general probl ..."
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Cited by 64 (6 self)
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We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NPhard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes. For bigger instances, the iterated barycenter method turns out to be the method of choice among several popular heuristics whose performance we could assess by comparing their results to optimum solutions.