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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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Ýmir Vigfússon IBM Research Haifa Labs Ken Birman Cornell University Qi Huang Cornell University Deepak Nataraj Cornell University.

Ýmir Vigfússon IBM Research Haifa Labs Ken Birman Cornell University Qi Huang Cornell University Deepak Nataraj Cornell University.

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