Stability in the self-organized evolution of networks

Jansen, Thomas; Theile, Madeleine

doi:10.1145/1276958.1277147

Cited by 6 publications

(16 citation statements)

References 12 publications

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“…The variety of results may be seen as a demonstration of this framework's generality. Parts of the results added here have already been presented at a conference [10].…”

Section: Our Resultsmentioning

confidence: 99%

Stability in the Self-Organized Evolution of Networks

Theile

Jansen

2008

Algorithmica

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The modeling and analysis of large networks of autonomous agents is an important topic with applications in many different disciplines. One way of modeling the development of such networks is by means of an evolutionary process. The autonomous and selfishly acting agents are randomly chosen to become active according to an underlying probability distribution. They may apply some kind of local mutation operator to the network and decide about accepting these changes via some fitness-based selection whereas the fitness models the agent's preferences. This general framework for the self-organized evolution of networks can be instantiated in many different ways. For interesting instances, one would like to know whether stable topologies eventually evolve and how long this process may take. Here, known results for an instantiation based on random spanning trees and a fitness-based selection according to global graph centrality measures are improved. Moreover, a more natural and local fitness-based selection using only the information on nearest neighbors is presented and analyzed with respect to the expected time needed to reach a stable state.Peer reviewe

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“…The variety of results may be seen as a demonstration of this framework's generality. Parts of the results added here have already been presented at a conference [10].…”

Section: Our Resultsmentioning

confidence: 99%

Stability in the Self-Organized Evolution of Networks

Theile

Jansen

2008

Algorithmica

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“…Although some facts are known about similar algorithms for the case of trees ( [5], [6]) not much literature is devoted to considering graphs with the total number of edges acceding n − 1 where n is the number of nodes in the network. In this work we have established a simple bound on the one-step improvement/worsening of the algorithm and also have shown that the algorithm is ergodic, meaning that with positive probability it doesn't get stuck at a local optima.…”

Section: Discussionmentioning

confidence: 99%

“…The algorithm (which is also introduced in [5] for the case of trees) works as follows: 1) Select a, b ∈ V according to μ.…”

Section: B the Description Of The Algorithmmentioning

confidence: 99%

“…It should be noted that the algorithm itself is not new. A similar algorithm when applied for the special type of networks (trees) has been analyzed for some special problems in [5] and [6]. It should also be noted that the optimal communication arrangement problem has been extensively studied in the literature particularly for the case of trees [3], [4].…”

Section: Introductionmentioning

confidence: 99%

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Preliminary theoretical analysis of a local search algorithm to optimize network communication subject to preserving the total number of links

Mitavskiy

Rowe

Cannings

2008

2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)

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A variety of phenomena such as world wide web, social or business interactions are modeled by various kinds of networks (such as the scale free or preferential attachment networks). However, due to the model-specific requirements one may want to rewire the network to optimize the communication among the various nodes while not overloading the number of channels (i.e. preserving the number edges). In the current paper we present a formal framework for this problem and a simple heuristic local search algorithm to cope with it. We estimate the expected single-step improvement of our algorithm, establish the ergodicity of the algorithm (i.e. that the algorithm never gets stuck at a local optima) with probability 1) and we also present a few initial empirical results for the scale free networks.

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“…Related work. The model and the philosophy in this paper are related to the network creation game [19,13,32,1,37]. Fabrikant et al [19] was the first to introduce the network creation game, in order to understand the evolution of network topologies by selfish agents.…”

Section: Introductionmentioning

confidence: 99%

The Emergence of Sparse Spanners and Greedy Well-Separated Pair Decomposition

Gao

Zhou

2010

Lecture Notes in Computer Science

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A spanner graph on a set of points in R d contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. A spanner with a sparse set of edges is thus a good candidate for network backbones, as desired in many practical scenarios such as the transportation network and peer-to-peer network overlays. In this paper we investigate new models and aim to interpret why good spanners 'emerge' in reality, when they are clearly built in pieces by agents with their own interests and the construction is not coordinated. Our main result is to show that the following algorithm generates a (1 + ε)-spanner with a linear number of edges, constant average degree, and the total edge length as a small logarithmic factor of the cost of the minimum spanning tree. In our algorithm, the points build edges at an arbitrary order. When a point p checks on whether the edge to a point q should be built, it will build this edge only if there is no existing edge p ′ q ′ with p ′ and q ′ at distances no more than 1 4(1+1/ε) · |p ′ q ′ | from p, q respectively. Eventually when all points have finished checking edges to all other points, the resulted collection of edges forms a sparse spanner as desired. This new spanner construction algorithm can be extended to a metric space with constant doubling dimension and admits a local routing scheme to find the short paths.As a side product, we show a greedy algorithm for constructing linear-size well-separated pair decompositions that may be of interest on its own. A well-separated pair decomposition is a collection of subset pairs such that each pair of point sets is fairly far away from each other compared with their diameters and that every pair of points is 'covered' by at least one well-separated pair. Our greedy algorithm selects an arbitrary pair of points that have not yet been covered and puts a 'dumb-bell' around the pair as the well-separated pair, repeats this until all pairs of points are covered. When the algorithm finishes, we show only a linear number of pairs is generated, which is asymptotically optimal.

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Stability in the self-organized evolution of networks

Cited by 6 publications

References 12 publications

Stability in the Self-Organized Evolution of Networks

Stability in the Self-Organized Evolution of Networks

Preliminary theoretical analysis of a local search algorithm to optimize network communication subject to preserving the total number of links

The Emergence of Sparse Spanners and Greedy Well-Separated Pair Decomposition

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