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Trading accuracy for speed in approximate consensus

Published online by Cambridge University Press:  17 November 2016

Jacob Beal
Jacob Beal*
Affiliation:
Raytheon BBN Technologies, Cambridge, MA 02138, USA e-mail: [email protected]
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Abstract

Approximate consensus is an important building block for distributed systems, used overtly or implicitly in applications as diverse as formation control, sensor fusion, and synchronization. Laplacian-based consensus, the current dominant approach, is extremely accurate and resilient, but converges slowly. Comparing Laplacian-based consensus to exact consensus algorithms, relaxing the requirements for accuracy and resilience should enable a spectrum of algorithms that incrementally tradeoff accuracy and/or resilience for speed. This manuscript demonstrates that may be so by beginning to populate this spectrum with a new approach to approximate consensus, Power-Law-Driven Consensus (PLD-consensus), which accelerates consensus by sending values across long distances using a self-organizing overlay network. Both a unidirectional and bidirectional algorithm based on this approach are studied. Although both have the same asymptotic O(diameter) convergence time (vs. O(diameter 2) for Laplacian-based), unidirectional PLD-consensus is faster and more resilient than bidirectional PLD-consensus, but exhibits higher variance in the converged value.

Type
Articles
Information
The Knowledge Engineering Review , Volume 31 , Special Issue 4: Spatial Computing , September 2016 , pp. 325 - 342
Copyright
© Cambridge University Press, 2016 

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