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

Virtual Network Mapping based on Subgraph Isomorphism Detection Jens Lischka, Holger Karl Paderborn University 23.09.2009 Jens Lischka 1

VNM Problem VNR 1(t 0 , 10) PN 2 6 7 5 2 5 4 5 β β G B β C 4 15 0 4 5 5 0 5 γ 7 3 3 α F 2 7 3 0 4 3 α 3 α A D γ E 3 3 0 0 8 8 5 7 0 0 VNR 2(t 5 ,3) VNR 3(t 6 ,3) β α β α 15 8 3 5 3 2 23.09.2009 Jens Lischka 2

Overview • 2stage VNM algorithm • Subgraph Isomorphism Detection based VNM • Experimental results 23.09.2009 Jens Lischka 3

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 6 6 7 0 5 4 5 0 β G B C γ 4 15 10 5 0 5 4 5 γ 7 3 0 3 β F 7 3 1 4 3 α 3 A D E α 4 1 4 8 8 5 7 0 23.09.2009 Jens Lischka 4

2stage vs. vnmFlib 2stage vnmFlib Map single node n Map nodes Map links No No Map ninks connected to n complete valid valid Yes No Yes Yes Track back to last valid mapping Done! Done! 23.09.2009 Jens Lischka 5

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. Subgraph Mapping C={ α , γ , β } M={A} 6 6 7 5 4 5 β 4 G B C 15 5 5 5 4 3 γ 3 7 F 7 3 4 3 α α 3 A D E α 4 4 8 0 5 7 8 8 23.09.2009 Jens Lischka 6

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. Subgraph Mapping C={ γ , β } M={B,E,F} 6 6 7 0 5 4 5 β 4 G γ B C 15 2 5 4 5 5 3 γ γ 7 7 F 7 3 3 4 3 3 α α 3 A D E α 0 4 4 5 7 8 23.09.2009 Jens Lischka 7

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. Subgraph Mapping C={ β } M={G,E,F} 6 6 6 0 0 5 0 4 5 β β 4 4 G β γ B C 15 2 4 5 3 5 5 c γ 7 7 F 7 3 ‐ 2 3 4 3 3 a α 3 A D E α 0 4 4 5 7 8 23.09.2009 Jens Lischka 8

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. Subgraph Mapping C={b} M={G,E,F} 6 6 6 0 5 4 5 β β 4 4 G γ B C 15 5 2 4 0 3 5 5 c γ 7 7 3 F 7 3 4 3 3 a α 3 A D E α β 0 4 4 ‐ 1 ‐ 1 5 7 8 1 23.09.2009 Jens Lischka 9

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. Subgraph Mapping C={ γ , β } M={B,E} 6 6 7 5 4 5 β 4 G B C 15 5 5 4 3 c γ 7 7 3 F 7 5 3 4 3 3 a α 3 A D E γ α 0 4 4 1 1 5 7 8 0 23.09.2009 Jens Lischka 10

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. Subgraph Mapping C={ β } M={B,F,G} 6 6 6 7 5 1 4 5 β β 4 4 G B β C 15 5 4 5 0 3 5 5 c γ 7 7 F 3 7 3 4 0 3 3 a α 3 A D γ E α 0 1 1 5 0 8 23.09.2009 Jens Lischka 11

Path Splitting • Split up path into multiple paths 6 7 5 5 4 5 8 G B C 15 VNR 5 5 5 4 3 3 F α 8 3 α β 4 3 8 8 8 3 A D E β 4 4 3 3 8 5 7 23.09.2009 Jens Lischka 12

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 23.09.2009 Jens Lischka 13

Experimental results 23.09.2009 Jens Lischka 14

Experimental Results 23.09.2009 Jens Lischka 15

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 on the PlanetLabTestbed infrastructure as part of the OneLab2 project. 23.09.2009 Jens Lischka 16

Thank You Questions? 23.09.2009 Jens Lischka 17

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. 23.09.2009 Jens Lischka 18

VNM Algorithms • Virtual Network Embedding with Coordinated Node and Link Mapping. – In Proceedings of the 28 th Conference on Computer Communications (IEEE INFOCOMM), April 2009. 23.09.2009 Jens Lischka 19

SID based VNM • Idea: Map Nodes and Links alternately based on 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 23.09.2009 Jens Lischka 20