Abstract
The dominant eigenvector of matrices defined by weighted links in overlay networks plays an important role in many peer-to-peer applications. Examples include trust management, importance ranking to support search, and virtual coordinate systems to facilitate managing network proximity. Robust and efficient asynchronous distributed algorithms are known only for the case when the dominant eigenvalue is exactly one. We present a fully distributed algorithm for a more general case: non-negative square matrices that have an arbitrary dominant eigenvalue. The basic idea is that we apply a gossip-based aggregation protocol coupled with an asynchronous iteration algorithm, where the gossip component controls the iteration component. The norm of the resulting vector is an unknown finite constant by default; however, it can optionally be set to any desired constant using a third gossip control component. Through extensive simulation results on artificially generated overlay networks and real web traces we demonstrate the correctness, the performance and the fault tolerance of the protocol.
This work was completed while Márk Jelasity was with the University of Bologna. This work was partially supported by the Future and Emerging Technologies unit of the European Commission through Project DELIS (IST-2002-001907).
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Jelasity, M., Canright, G., Engø-Monsen, K. (2007). Asynchronous Distributed Power Iteration with Gossip-Based Normalization. In: Kermarrec, AM., Bougé, L., Priol, T. (eds) Euro-Par 2007 Parallel Processing. Euro-Par 2007. Lecture Notes in Computer Science, vol 4641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74466-5_55
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