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APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Efficient broadcasting in random power law networks
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Ultra-fast rumor spreading in social networks
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Broadcasting algorithms have various range of applications in different fields of computer science. In this paper we consider randomized broadcasting algorithms in power law graphs which are often used to model large scale real world networks such as the Internet. We prove that for certain (truncated) power law networks there exists a time efficient randomized broadcasting algorithm whose communication complexity is bounded by an asymptotically optimal value. In order to describe these power law graphs, we first consider the generalized random graph model G(d) = (V,E), where d = (d1, ..., dn) is a given sequence of expected degrees, and two nodes vi,vj ∈V share an edge in G(d) with probability pi,j = didj /∑$_{k=1}^{n}$dk, independently [7]. We show for these graphs that if the expected minimal degree dmin is larger than logδn, δ2, and the number of nodes with expected degree di is proportional to (di – dmin+1)−β, where β2 is a constant, then a simple randomized broadcasting protocol exists, which spreads any information r to all nodes of a graph G(d) within O(logn) steps by using at most O(n max{ loglogn, logn/logdmin}) transmissions. Furthermore, we discuss the applicability of our methods in more general power law graph models. Please note that our results hold with probability 1– 1/nΩ(1), even if n and d are completely unknown to the nodes of the graph. The algorithm we present in this paper uses a very simple communication rule, and can efficiently handle restricted node failures or dynamical changes in the size of the network. In addition, our methods might be useful for further research in this field.