1. Hardness of Approximation and Greedy Algorithms for the Adaptation Problem in Virtual Environments Ananth I. Sundararaj, Manan Sanghi, John R. Lange and Peter A. Dinda {ais,manan,jarusl,pdinda}@cs.northwestern.edu Prescience Lab Department of Electrical Engineering and Computer Science Northwestern University

2. 2 Summary Virtual execution environments provide opportunities for dynamic adaptation Important components are –Resource monitoring and inference –Application independent adaptation mechanisms –Efficient adaptation algorithms In this work –Formalize the adaptation problem –Show that it is NP-hard –Prove that it is NP-hard to approximate –Evaluate greedy heuristics

3. 3 Aim Grid Computing New Paradigm Traditional Paradigm Deliver arbitrary amounts of computational power to perform distributed and parallel computations Problem1: Grid Computing using virtual machines Problem2: Solution How to leverage them? Virtual Machines What are they? 6b 6a 5 4 3b 3a 2 1 Resource multiplexing using OS level mechanism Complexity from resource user’s perspective Complexity from resource owner’s perspective Virtual Machine Grid Computing

4. 4 Virtual Machines Virtual machine monitors (VMMs) Raw machine is the abstraction VM represented by a single image VMware GSX Server

5. 5 The Simplified Virtuoso Model Orders a raw machine User Specific hardware and performance Basic software installation available User’s LAN VM Virtual networking ties the machine back to user’s home network Virtuoso continuously monitors and adapts

6. 6 User’s friendly LAN Foreign hostile LAN Virtual Machine VNET: A bridge with long wires Host Proxy X Virtual Networks VM traffic going out on foreign LAN IP network A machine is suddenly plugged into a foreign network. What happens? Does it get an IP address? Is it a routeable address? Does firewall let its traffic through? To any port?

7. 7 Measurement and Inference Application (VTTIF) Topology Traffic load Underlying network layer Physical hosts Virtual network layer VNET daemons Application layer VM layer Host and VM Size and compute capacities Size and compute demands Topology Bandwidth Latency Underlying network [Gupta et al. LNCS 05] [Gupta et al. IPDPS 06]

8. 8 Adaptation Mechanisms Resource reservation Network CPU Resource reservation Physical hosts Topology changes VNET daemons VM Migration VM layer Topology changes Overlay links Overlay forwarding rules VM Migration Third party migration schemes X X X [Sundararaj et al. LCR 04, HPDC 05] [Lange et al. HPDC 05] [Lin et al. GRID 2004]

9. 9 Infer application’s resource demands Measure physically available resources Algorithm matches demands to resources Adaptation mechanisms Defined objective function is optimized Any Adaptation Scheme Adaptation in Virtuoso VTTIF Infers application’s demands Wren measures available resources Algorithm matches demands to resources VM Migration, Topology, routing, Resource reservation Maximizes sum of residual bottleneck bandwidths input by driving that by driving such that input Adaptation in Virtuoso

10. 10 Optimization Problem Given the –network traffic load matrix of the application –computational intensity in each VM –topology of the network –load on its links, routers and hosts What is the –mapping of VMs to hosts –overlay topology connecting the hosts –forwarding rules on that topology –required CPU and network reservations That –maximizes the application performance?

11. 11 Problem Formulation (MARPVEE) Mapping and Routing Problem in Virtual Execution Environments Measured data Application demands VM to host mapping Constraints Objective function

12. 12 Theorem 1: MARPVEED (decision version) is NP-complete. The NP-hardness is established by reduction from the Edge Disjoint Path Problem (EDPP) A simpler problem with only the routing component (RPVEED) is shown to be NP-complete Theorem 2: For any δ> 0, it is NP-hard to approximate MARPVEE within m 1/2- δ unless P=NP. EDPP is used to investigate the approximability of MARPVEE. m is the number of edges in the virtual overlay graph Results

13. 13 Greedy Adaptation Algorithms Devised two greedy algorithms for mapping VMs to hosts 1.Finds all mappings in a single pass (GreedyMapOne) 2.Other takes two passes over input data (GreedyMapTwo) Adapted Dijkstra’s shortest path algorithm Finds widest path for an unsplittable network flow (GreedyRouting) MARPVEE involves both, mapping and routing network flows First apply the mapping algorithm (either one) followed by the routing algorithm Alternatively we can interleave the two

14. 14 IP network Illinois, USA 100 Mbit backplane internal bandwidth 11 MB/sec 0.89 1.58 1.76 Virginia, USA 100 Mbit backplane internal bandwidth 10 MB/sec Pittsburgh, USA Numbers indicate end-to-end available bandwidth (MB/sec) between the different locations vm3 vm4vm5 vm2 vm7 vm6 vm8 vm1 0.70.98 0.7 0.98 0.59 1.3 0.56 0.750.56 0.33 An application consisting of two disjoint pieces executing inside of the virtual machines (VMs). The numbers indicate the bandwidth (MB/sec) demand among the communicating pairs Physical Topology Application Topology Mapping an application topology onto a physical topology

15. 15 Evaluation Implemented an evaluator to calculate the residual bandwidth for multiple test cases We evaluated the four algorithm variations in three different settings –randomly generated topologies using BRITE –smaller topologies created by hand –a real world scenario All the algorithms were found to perform well in most scenarios. For randomly generated topologies we do not see any differences between the different variations. However for the topology created by hand and for the real world scenario that result in a clustered setting, the one-pass variation outperforms the two-pass algorithm. Further, we did not notice in difference between the interleaved and non-interleaved variations.

16. 16 Please visit –Virtuoso: Resource Management and Prediction for Distributed Computing using Virtual Machines http://virtuoso.cs.northwestern.edu –Prescience Lab (Northwestern University) http://plab.cs.northwestern.edu For More Information