An Optimal Broadcast Algorithm for Content-Addressable Networks Ludovic Henrio Fabrice Huet Justine Rochas 1 18/12/ OPODIS (Nice)

Background Efficient Algorithm Experiments 2

General Motivation – RDF Storage  Context  Web Semantic: RDF data  Challenge  Store and retrieve RDF data  Large scale setting  Our solution  Content Addressable Network 3

Content-Addressable Networks (CAN)  Overlay network  Nodes are peers A E B C D 01 1 dim #1 dim #2 4  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

Problem: Cost of Queries 5 2 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 NOT OK

 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 01 1 dim #1 dim #2 Problem: Duplicated Messages 6

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 7 [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 B C

M-CAN Execution INIT 8 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

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 messages sending only when reaching a « border » 9 [3] Francesco Bongiovanni, Ludovic Henrio: A Mechanized Model for CAN Protocols. FASE 2013

Background Efficient Algorithm Experiments 10

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 11 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 recursively 12 spatial constraint in 3D CAN spatial constraint in 2D CAN

 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 13

Efficient Algorithm – Execution INIT 14 Corner Constraint Message Message that leads to duplication Spatial Constraint

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 15 This algorithm is optimal All peers receive a broadcast message exactly once

Background Efficient Algorithm Experiments 16

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 17 A C B

Number of messages 18 Maximum gain of 5.3 MB

Number of messages 19

Execution Time 20 Significant speedup

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 ! 21 [4] EventCloud A range multicast

22 dim #1 dim #3 dim #2