Virtual Network Mapping based on Subgraph Isomorphism Detection Jens - - PowerPoint PPT Presentation

Jens Lischka 23.09.2009 1

Virtual Network Mapping based on Subgraph Isomorphism Detection

Jens Lischka, Holger Karl Paderborn University

Jens Lischka 23.09.2009 2

VNM Problem

VNR 1(t0, 10) 2 β α γ 5 4 3 7 8 PN A F C E B D G 3 4 5 15 3 3 3 6 5 5 5 4 3 3 7 8 7 7 α γ β 5 VNR 2(t5,3) 3 β α 15 5 α β 2 2 VNR 3(t6,3) 3 β α 8 2 4 5

Jens Lischka 23.09.2009 3

Overview

• 2stage VNM algorithm
• Subgraph Isomorphism Detection based VNM
• Experimental results

Jens Lischka 23.09.2009 4

2stage Algorithm

1. First stage: find suitable mapping nodes 2. Second stage: find a link mapping (k‐shortest paths, multi commodity flow) 3. No paths for virtual links β‐>γ! 4. Problem: first stage does not take connectivity of VNs into account

VN PN A 6 β α γ 5 4 3 7 8 F C E B D G 3 5 4 5 15 3 3 4 3 6 8 5 7 5 7 4 4 7 α γ β 4 5 10 1 1

Jens Lischka 23.09.2009 5

2stage vs. vnmFlib

Map nodes Map ninks valid No Yes Map single node n Map links connected to n valid Track back to last valid mapping complete Yes Yes No No Done! Done! 2stage vnmFlib

Jens Lischka 23.09.2009 6

Example: vnmFlib

1. Compute set of candidates C. 2. Compute a set of mapping candidates M. 3. Add α to the subgraph and map it onto A. 4. Map all links connecting α with the subgraph onto the PN 5. Check validity.

α Subgraph Mapping 8 5 7 A F C E B D G 3 5 4 5 15 3 3 4 3 6 5 7 4 4 7 α β γ 6 5 4 3 7 8 α 8 C={α,γ,β} M={A} 4 5

Jens Lischka 23.09.2009 7

Example: vnmFlib

1. Compute C and M. 2. Add γ to the subgraph and map it onto B. 3. Map all links connecting γ with the subgraph onto the PN. 4. Check validity.

α Subgraph Mapping 5 7 A F C E B D G 3 5 4 5 15 3 3 4 3 6 5 7 4 4 7 α β γ 6 5 4 3 7 α γ γ 3 8 7 C={γ,β} M={B,E,F} 4 5 2

Jens Lischka 23.09.2009 8

Example: vnmFlib

1. Compute C and M. 2. Add β to the subgraph and map it onto G. 3. Map all links connecting β with the subgraph onto the PN. 4. Check validity.

a Subgraph Mapping 5 7 A F C E B D G 3 2 4 5 15 3 3 4 3 6 5 4 4 7 α β c 6 5 4 3 7 α γ γ 3 7 C={β} M={G,E,F} 8 β β 6 4 5 4 5 ‐2

Jens Lischka 23.09.2009 9

Example: vnmFlib

1. Choose next node E of M. 2. Map β onto E. 3. Map all links connecting β with the subgraph onto the PN. 4. Check validity.

a Subgraph Mapping 5 7 A F C E B D G 3 2 4 5 15 3 3 4 3 4 4 6 5 7 α β c 6 5 4 3 7 α γ γ 3 7 C={b} M={G,E,F} 8 β β 6 4 5 4 5 1 ‐1 ‐1

Jens Lischka 23.09.2009 10

Example: vnmFlib

1. Track back to the last valid mapping solution. 2. Choose next node E. 3. Map γ onto E. 4. Map all links connecting γ with the subgraph onto the PN. 5. Check validity.

a Subgraph Mapping 5 7 A F C E B D G 3 5 4 5 15 3 3 4 3 6 5 7 4 4 7 α β c 6 5 4 3 7 α γ γ 3 7 C={γ,β} M={B,E} 8 4 5 1 1

Jens Lischka 23.09.2009 11

Example: vnmFlib

1. Compute C and M. 2. Add β to the subgraph and map it onto B. 3. Map all links connecting β with the subgraph onto the PN. 4. Check validity.

a Subgraph Mapping 5 A F C E B D G 3 5 4 5 15 3 3 4 3 6 5 7 1 1 7 α β c 6 5 4 3 7 α γ γ 3 7 C={β} M={B,F,G} 8 β β 6 5 4 4 5 1

Jens Lischka 23.09.2009 12

Path Splitting

• Split up path into multiple paths

8 5 7 A F C E B D G 3 5 4 5 15 3 3 4 3 6 5 7 4 4 8 β 4 5 VNR 8 α β 8 8 α 3 3 3 5 5 8

Jens Lischka 23.09.2009 13

Experimental Results

• Network setup similar to previous work[1] with GT‐ITM tool:

– PN: 100 nodes and 500 links CPU at the nodes, Bandwidth at the links follow uniform distribution from 0‐100 units – VNs: 20‐40 nodes, each pair of nodes connected with probability 0.5 CPU and Bandwidth follow a uniform distribution from 0 to beta units.

• Compared our algorithm with the two stage VN Mapper of

[1].

[1]Rethinking Virtual Network Embedding: Substrate Support for Path Splitting and

• Migration. SIGCOMM Comput. Commun. Rev., 38(2):17‐29, 2008.

Source code available: http://www.princeton.edu/~minlanyu/embed.tar.gz

Jens Lischka 23.09.2009 14

Experimental results

Jens Lischka 23.09.2009 15

Experimental Results

Jens Lischka 23.09.2009 16

Summary

• Introduced new VNM method based on SID
• SID based VNM performs better than the

2stage approach

– Especially for higher beta values and bigger networks

• Currently we are implementing the mapper
• n the PlanetLabTestbed infrastructure as

part of the OneLab2 project.

Jens Lischka 23.09.2009 17

Thank You

Questions?

Jens Lischka 23.09.2009 18

VNM Algorithms

• 2stage:

– Rethinking Virtual Network Embedding: Support for Path Splitting and

• Migration. SIGCOMM, 2008.

– Algorithms for Assigning Substrate Network Resources to Virtual Network Components, INFOCOMM, 2006. – A Multi‐Commodity Flow Based Approach to Virtual Network Resource Allocation. GLOBECOMM, 2003.

• Simulated Annealing:

– A Solver for the Network Testbed Mapping Problem. Computer Communications Review 33(2), 2003.

• Mixed Integer Quadratic Program

– Efficient Mapping of Virtual Networks onto a shared Substrate. Technical Report, Washington University.

Jens Lischka 23.09.2009 19

VNM Algorithms

• Virtual Network Embedding with Coordinated

Node and Link Mapping.

– In Proceedings of the 28th Conference on Computer Communications (IEEE INFOCOMM), April 2009.

Jens Lischka 23.09.2009 20

SID based VNM

• Idea: Map Nodes and Links alternately based
• n vFlibSubgraph Isomorphism Detection

algorithm.

• Build a subgraph S of VN by successively

adding nodes of VN to S and map S onto PN until S fully covers VN.

• Difference to vFlib:

– Allow mapping of virtual links onto paths – Check capacity constraints