Minimum Dominating Sets in Scale-Free Network Ensembles

Molnár, Ferenc; Sreenivasan, Sameet; Szymański, Bolesław K.; Korniss, G.

doi:10.1038/srep01736

Cited by 54 publications

(46 citation statements)

References 31 publications

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“…We keep the average degree z = 10. For the generation of uncorrelated SF networks [35,36] (N = 10 4 , z = 10, with power law constant γ = 3) we employ the configuration model [36,37] with a structural cut-off, and a maximum possible node degree set to √ N , using a high accuracy look-up table from [38].…”

Section: Network Structuresmentioning

confidence: 99%

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The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators

et al. 2015

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The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes’ thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. We demonstrate that for a given size of the initiator set, there is a specific variance of the threshold distribution for which an opinion spreads optimally. Furthermore, in the case of synthetic graphs we show that the spread asymptotically becomes independent of the system size, and that global cascades can arise just by the addition of a single node to the initiator set.

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Section: Network Structuresmentioning

confidence: 99%

“…The authors are grateful to Ferenc Molnár Jr. for his assistance on the generation of scale-free networks with the desired and accurate cutoffs and average degree [38].…”

Section: Acknowledgmentsmentioning

confidence: 99%

The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators

et al. 2015

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“…Applying this local-consensus mechanism to the ER network of Fig. 2, the server fraction of obtained solutions is n 1 ≈ 0.140, which is a big drop as compared with the server fraction of n 1 ≈ 0.240 of the best-response mechanism, and it is only slightly beyond the server fraction of Comparing the performances of the local-consensus selection mechanism and the greedy highest-impact algorithm [28,31,32] on an ER network of N = 10 5 nodes and M = 5 × 10 5 links. Each histogram P (n1) of server fraction n1 is obtained by sampling 960 independent solutions.…”

Section: The Local-consensus Mechanismmentioning

confidence: 98%

Serving by local consensus in the public service location game

Sun

Zhou

2016

Sci Rep

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We discuss the issue of distributed and cooperative decision-making in a network game of public service location. Each node of the network can decide to host a certain public service incurring in a construction cost and serving all the neighboring nodes and itself. A pure consumer node has to pay a tax, and the collected tax is evenly distributed to all the hosting nodes to remedy their construction costs. If all nodes make individual best-response decisions, the system gets trapped in an inefficient situation of high tax level. Here we introduce a decentralized local-consensus selection mechanism which requires nodes to recommend their neighbors of highest local impact as candidate servers, and a node may become a server only if all its non-server neighbors give their assent. We demonstrate that although this mechanism involves only information exchange among neighboring nodes, it leads to socially efficient solutions with tax level approaching the lowest possible value. Our results may help in understanding and improving collective problem-solving in various networked social and robotic systems.

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“…However, e.g. van der Hofstad remarks, that true values of might be higher, because some estimates are biased [19], and even supporters admits that exceptional cases α < 2 are known [6], [8]. For example, in [5] the scaling exponent for an outdegree distribution of Internet graph is only γ = −1.75.…”

Section: Vertex Degree Distributionmentioning

confidence: 99%

Quantitative Analysis of the Internet Topology Model

Bernat

Čičák

2015

2015 4th Eastern European Regional Conference on the Engineering of Computer Based Systems

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The article presents analysis of the Internet topology graph model. We use usual methods to analyse properties of the model but also propose some new characteristics. Our experimental data set comprises long-term traceroute records for several thousands of target hosts, repeatedly executed from a fixed source. We processed particular routes by merging them all together thus creating a single connected graph, which represents a sample of Internet-like network. We evaluate several network characteristics, notably node degree distribution, k-core decomposition, clustering coefficients, etc. Comparison shows good correspondence with other known results.Furthermore, we examine new metrics, particularly the count and length of linear subgraphs and the number of connections between vertices with maximum and minimum degree. These characteristics help to distinguish between network types. The latter one appears to be useful also in the context of finding a dominating vertex set problem.

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Minimum Dominating Sets in Scale-Free Network Ensembles

Cited by 54 publications

References 31 publications

The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators

The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators

Serving by local consensus in the public service location game

Quantitative Analysis of the Internet Topology Model

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