hardness of approximation and greedy algorithms for the adaptation problem in virtual environments
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Hardness of Approximation and GreedyAlgorithms 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
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
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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
3b3a
2
1
Resource multiplexing using OS level mechanism
Complexity from resource user’s perspective
Complexity from resource owner’s perspective
Virtual Machine Grid Computing
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Virtual Machines
Virtual machine monitors (VMMs)
•Raw machine is the abstraction
•VM represented by a single image
•VMware GSX Server
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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
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User’s friendlyLAN
Foreign hostile LAN
Virtual Machine
VNET: A bridge with long wires
Host
Proxy
X
Virtual NetworksVM 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?
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Measurement and Inference
Application (VTTIF)• Topology
• Traffic load
Underlying network layer Physical hosts
Virtual network layerVNET daemons
Application layerVM 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]
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Adaptation Mechanisms
Resource reservation• Network
• CPU
Resource reservationPhysical hosts
Topology changesVNET daemons
VM MigrationVM layer
Topology changes • Overlay links
• Overlay forwarding rules
VM Migration• Third party migration schemes
X
XX
[Sundararaj et al. LCR 04, HPDC 05]
[Lange et al. HPDC 05]
[Lin et al. GRID 2004]
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Infer application’s resource demands
Measure physicallyavailable 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
input
by driving
that by driving
such that
input
input
Adaptation in Virtuoso
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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?
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Problem Formulation (MARPVEE)Mapping and Routing Problem in Virtual Execution Environments
Measured data
Application demands
VM to host mapping
Constraints
Objective function
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• 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 m1/2- 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
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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
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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
0.7 0.98
0.7
0.98
0.59
1.3 0.56
0.75 0.56
0.56 0.560.33
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
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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.