18/12/2013 - OPODIS (Nice)

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An Optimal Broadcast Algorithm for Content-Addressable NetworksLudovic Henrio

Fabrice Huet

Justine Rochas

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BackgroundEfficient AlgorithmExperiments

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General Motivation – RDF Storage

Context Web Semantic: RDF data

Challenge Store and retrieve RDF data Large scale setting

Our solution Content Addressable Network

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Content-Addressable Networks (CAN)

Overlay network Nodes are peers

AE

BC

D

0 1

1

dim #1

dim #2

Structured organization Multidimensional Cartesian space Entirely partitioned

A zone is managed by one peer A zone = a (hyper)rectangle

Neighborhood based on adjacent zones Routing = successively approaching value in all dimensions

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Problem: Cost of Queries2 queries over 2 variables:

conjunction of two 2-dimensional broadcast

1 query over 2 variables

1 query over 1 variable

Naive broadcast does not scale

OK

OK

NOT OK

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Duplicated messages 11 peers 40 messages !

How to eliminate duplicates? For each peer P Find the peer that is reponsible

for sending the message to P

E

0 1

1

dim #1

dim #2

Problem: Duplicated Messages

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Existing Solutions Use the CAN structure to route messages

Meghdoot [1] « upperLeft » predicate M-CAN [2]

M-CAN principles Initiator peer sends to all neighbors Other peers forward to neighbors on

Same dimension on opposite side Lower dimensions on all sides

Forwarding on the last dimension depends on a constraint

[1] A. Gupta, O. D. Sahin, D. Agrawal, A. El Abbadi: Meghdoot: Content-Based Publish/Subscribe over P2P Networks. Middleware 2004

Meghdoot: start from a corner

A

BC

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M-CAN Execution

INIT

Corner Constraint

Message

Message that leads to duplication

[2] S. Ratnasamy, M. Handley, R. M. Karp, S. Shenker: Application-Level Multicast Using Content-Addressable Networks. Networked Group Communication 2001

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Preliminary Work

Existence of an optimal algorithm proved [3]

A solution to exhibit existence Valid for a very generic definition of CAN Not efficient (execution time)

Parallelize messagessending only whenreaching a « border »

INIT

[3] Francesco Bongiovanni, Ludovic Henrio: A Mechanized Model for CAN Protocols. FASE 2013

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BackgroundEfficient AlgorithmExperiments

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Hypothesis and Goals

CAN = adjacent rectangles

No additional structure Tolerate churns between two Bcast

Not implementation-dependent Do not tolerate churns during Bcast

Optimal in number of messages and good parallelization

A spanning tree

INIT

Efficient Algorithm – Principle

Removes all duplicates In all dimensions

How ? Uses the corner constraint Plus a spatial constraint

A set of fixed values Reduce the problem

Applies recursivelyspatial constraint in 3D CAN

spatial constraint in 2D CAN

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Observation #1 Easy to forward in 1D

Observation #2 Only one zone touches a corner

Idea of the algorithm Suppose an efficient broadcast in dimension N Apply on a hyperplane of dimension N - 1 Send to both sides of this hyperplane using the corner

constraint Repeat until the hyperplane is just a line (dimension 1)

Efficient Algorithm

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Efficient Algorithm – Execution

INIT

Corner Constraint

Message

Message that leads to duplication

Spatial Constraint

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Efficient Algorithm – Properties Proved to be correct

All peers receive a broadcast message at least once

Proved to be minimal All peers receive a broadcast message at most once

Elements of proof – When receiving on dimension D: dim < D spatial constraint is satisfied For dim = D ascending or descending direction dim > D corner constraint is satisfied

This algorithm is optimal

All peers receive a broadcast message exactly once

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BackgroundEfficient AlgorithmExperiments

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Experimental Setup

Using the Grid5000 platform Multisite experimentation

Deployment From 50 to 1500 peers Up to 200 physical machines

CAN setting Successively split zones in half Zone to split is chosen randomly

AC

B

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Number of messages

Maximum gain of 5.3 MB

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Number of messages

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Execution Time

Significant speedup

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Conclusion: Broadcast on CAN

We found an optimal solution Proved to be correct and optimal Efficient on large scale settings

Support range multicast

Currently in use in the EventCloud project [4] Management of RDF data Algorithm used for one year Tested and approved !

[4] http://www.play-project.eu/solutions/event-cloud

EventCloud

A range multicast

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dim #1dim #3

dim #2