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Sliver: A fast distributed slicing algorithm Ymir Vigfusson Cornell University Ymir Vigfusson Cornell University Vincent Gramoli EPFL & UniNE Switzerland Anne-Marie Kermarrec INRIA Rennes France Vincent Gramoli EPFL & UniNE Switzerland Anne-Marie Kermarrec INRIA Rennes France Ken Birman Cornell University Robbert van Renesse Cornell University Ken Birman Cornell University Robbert van Renesse Cornell University Joint work with:

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The Distributed Slicing Problem n nodes, each has an attribute value x i n nodes, each has an attribute value x i 14575080839598

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The Distributed Slicing Problem n nodes, each has an attribute value x i n nodes, each has an attribute value x i Divide the sorted list of x i s into k slices Divide the sorted list of x i s into k slices n nodes, each has an attribute value x i n nodes, each has an attribute value x i Divide the sorted list of x i s into k slices Divide the sorted list of x i s into k slices 14575080839598

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The Distributed Slicing Problem n nodes, each has an attribute value x i n nodes, each has an attribute value x i Divide the sorted list of x i s into k slices Divide the sorted list of x i s into k slices Each node i wants to independently know to which of the k slices x i belongs Each node i wants to independently know to which of the k slices x i belongs n nodes, each has an attribute value x i n nodes, each has an attribute value x i Divide the sorted list of x i s into k slices Divide the sorted list of x i s into k slices Each node i wants to independently know to which of the k slices x i belongs Each node i wants to independently know to which of the k slices x i belongs 14575080839598

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The Distributed Slicing Problem n nodes, each has an attribute value x i n nodes, each has an attribute value x i Divide the sorted list of x i s into k slices Divide the sorted list of x i s into k slices Each node i wants to independently know to which of the k slices x i belongs Each node i wants to independently know to which of the k slices x i belongs n nodes, each has an attribute value x i n nodes, each has an attribute value x i Divide the sorted list of x i s into k slices Divide the sorted list of x i s into k slices Each node i wants to independently know to which of the k slices x i belongs Each node i wants to independently know to which of the k slices x i belongs 14575080839598 Im in slice 2!

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The Distributed Slicing Problem Large network with high rate of churn

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The Distributed Slicing Problem Large network with high rate of churn Example: Choosing super-peers in the network Large network with high rate of churn Example: Choosing super-peers in the network

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Sliver: Distributed slicing algorithm Each node i gossips x i (and other known values) to c random nodes

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Sliver: Distributed slicing algorithm Each node i gossips x i (and other known values) to c random nodes Node j keeps track of data it receives Value, sender, expiration time Suppose B j values out of m are below x j Each node i gossips x i (and other known values) to c random nodes Node j keeps track of data it receives Value, sender, expiration time Suppose B j values out of m are below x j

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Sliver: Distributed slicing algorithm Each node i gossips x i (and other known values) to c random nodes Node j keeps track of data it receives Value, sender, expiration time Suppose B j values out of m are below x j Node j estimates its slice as Each node i gossips x i (and other known values) to c random nodes Node j keeps track of data it receives Value, sender, expiration time Suppose B j values out of m are below x j Node j estimates its slice as

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ResultsResults All nodes know their slice within 1 w.h.p. after rounds in expectation All nodes know their slice within 1 w.h.p. after rounds in expectation

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ResultsResults All nodes know their slice within 1 w.h.p. after rounds in expectation Experiments on Emulab and simulations on Skype traces indicate rapid convergence and churn- tolerance Conclusion: Sliver is simple and robust with fast convergence properties. All nodes know their slice within 1 w.h.p. after rounds in expectation Experiments on Emulab and simulations on Skype traces indicate rapid convergence and churn- tolerance Conclusion: Sliver is simple and robust with fast convergence properties.

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20/10/2006ALPAGE1 Ordered slicing of very large scale overlay networks Mark Jelasity University of Bologna, Italy Anne-Marie Kermarrec INRIA Rennes/IRISA,

20/10/2006ALPAGE1 Ordered slicing of very large scale overlay networks Mark Jelasity University of Bologna, Italy Anne-Marie Kermarrec INRIA Rennes/IRISA,

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