Scale-free and stable structures in complex<i>ad hoc</i>networks

Sarshar, Nima; Roychowdhury, Vwani P.

doi:10.1103/physreve.69.026101

Cited by 99 publications

(91 citation statements)

References 6 publications

(16 reference statements)

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“…In general, for different c's the possible PL exponents (γ 1 , γ 2 ) are plotted in Fig. 2. (ii) Role of the Deletion Rate c: If Q = 1 then it is shown in [12] that for any deletion rate c > 0, the PL exponent is > 3, and that the exponent increases rapidly with an increase in c. As shown in Fig. 2, for two classes it is possible to have one class with PL exponent < 3.…”

Section: Approach and A Preview Of Resultsmentioning

confidence: 99%

“…It was shown in [12] that when |Q| = 1, i.e., there is only one class and the network is homogeneous, then γ is always greater than 3 for any deletion rate c > 0. Moreover, even for small values of c the exponent becomes quite large, and the network shows none of the characteristics associated with heavy-tailed PL degree distributions.…”

Section: Role Of Deletion Rate Cmentioning

confidence: 99%

“…We assume that there is no compensation, i.e., n 1 = n 2 = · · · = n Q = 0, and that the deletions of nodes are made uniformly over all the classes, i.e., c q = c * s q . Note that the homogeneous case, where there is only one class, i.e., |Q| = 1, was solved in [12]. Let i t;q be the set of all nodes of type q that are present in the network at time t. When a new link chooses a node i ∈ i t;q for connection, i can accept to attach to it with some probability d q and deny the attachment with probability 1 − d q .…”

Section: Nonuniform Attraction and Populationmentioning

confidence: 99%

“…We examine the effects of heterogenous compensation magnitudes for the lost links. In a compensation mechanism as introduced in [12], a node will react to losing a neighbor by initiating a number of new connections to compensate for its lost links. The number of such compensatory connections is an indication of the degree with which the node responds to its changes.…”

Section: Nonuniform Responsiveness (Nq)mentioning

confidence: 99%

“…The continuous rate equation approach [12,13] can now be employed to track k(i, t; q), at a time t ≥ i in the equivalent protocol:…”

Section: Nonuniform Attraction and Populationmentioning

confidence: 99%

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Multiple power-law structures in heterogeneous complex networks

Sarshar

Roychowdhury

2005

Phys. Rev. E

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This paper develops a framework for analyzing and designing dynamic networks comprising different classes of nodes that coexist and interact in one shared environment. We consider ad hoc (i.e., nodes can leave the network unannounced, and no node has any global knowledge about the class identities of other nodes) preferentially grown networks, where different classes of nodes are characterized by different sets of local parameters used in the stochastic dynamics that all nodes in the network execute. We show that multiple scale-free structures, one within each class of nodes, and with tunable power-law exponents (as determined by the sets of parameters characterizing each class) emerge naturally in our model. Moreover, the coexistence of the scale-free structures of the different classes of nodes can be captured by succinct phase diagrams, which show a rich set of structures, including stable regions where different classes coexist in heavy-tailed (i.e., exponent is between 2 and 3) and light-tailed (i.e., exponent is > 3) states, and sharp phase transitions. The topology of the emergent networks is also shown to display a complex structure, akin to the distribution of different components of an alloyed material; e.g., nodes with a light-tailed scale-free structure get embedded to the outside of the network, and have most of its edges connected to nodes belonging to the class with a heavy-tailed distribution. Finally, we show how the dynamics formulated in this paper will serve as an essential part of ad-hoc networking protocols, which can lead to the formation of robust and efficiently searchable networks (including, the well-known Peer-To-Peer (P2P) networks) even under very dynamic conditions.

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Section: Approach and A Preview Of Resultsmentioning

confidence: 99%

Section: Role Of Deletion Rate Cmentioning

confidence: 99%

Section: Nonuniform Attraction and Populationmentioning

confidence: 99%

Section: Nonuniform Responsiveness (Nq)mentioning

confidence: 99%

“…The continuous rate equation approach [12,13] can now be employed to track k(i, t; q), at a time t ≥ i in the equivalent protocol:…”

Section: Nonuniform Attraction and Populationmentioning

confidence: 99%

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Multiple power-law structures in heterogeneous complex networks

Sarshar

Roychowdhury

2005

Phys. Rev. E

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Modeling networked systems using the topologically distributed bounded rationality framework

2016

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In networked systems research, game theory is increasingly used to model a number of scenarios where distributed decision making takes place in a competitive environment. These scenarios include peer‐to‐peer network formation and routing, computer security level allocation, and TCP congestion control. It has been shown, however, that such modeling has met with limited success in capturing the real‐world behavior of computing systems. One of the main reasons for this drawback is that, whereas classical game theory assumes perfect rationality of players, real world entities in such settings have limited information, and cognitive ability which hinders their decision making. Meanwhile, new bounded rationality models have been proposed in networked game theory which take into account the topology of the network. In this article, we demonstrate that game‐theoretic modeling of computing systems would be much more accurate if a topologically distributed bounded rationality model is used. In particular, we consider (a) link formation on peer‐to‐peer overlay networks (b) assigning security levels to computers in computer networks (c) routing in peer‐to‐peer overlay networks, and show that in each of these scenarios, the accuracy of the modeling improves very significantly when topological models of bounded rationality are applied in the modeling process. Our results indicate that it is possible to use game theory to model competitive scenarios in networked systems in a way that closely reflects real world behavior, topology, and dynamics of such systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 123–137, 2016

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A model of self‐avoiding random walks for searching complex networks

et al. 2011

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Random walks have been proven useful in several applications in networks. Some variants of the basic random walk have been devised pursuing a suitable trade-off between better performance and limited cost. A self-avoiding random walk (SAW) is one that tries not to revisit nodes, therefore covering the network faster than a random walk. Suggested as a network search mechanism, the performance of the SAW has been analyzed using essentially empirical studies.A strict analytical approach is hard since, unlike the random walk, the SAW is not a Markovian stochastic process. We propose an analytical model to estimate the average search length of a SAW when used to locate a resource in a network. The model considers single or multiple instances of the resource sought and the possible availability of one-hop replication in the network (nodes know about resources held by their neighbors). The model characterize networks by their size and degree distribution, without assuming a particular topology. It is, therefore, a mean-field model, whose applicability to real networks is validated by simulation. Experiments with sets of randomly built regular networks, Erdős-Rényi networks, and scale-free networks of several sizes and degree averages, with and without one-hop replication, show that model predictions *

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Scale-free and stable structures in complexad hocnetworks

Cited by 99 publications

References 6 publications

Multiple power-law structures in heterogeneous complex networks

Multiple power-law structures in heterogeneous complex networks

Modeling networked systems using the topologically distributed bounded rationality framework

A model of self‐avoiding random walks for searching complex networks

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