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Bilal Gonen, Murat Yuksel, Sushil Louis University of Nevada, Reno

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Motivation & Problem definition: Intra- domain traffic engineering Black-box problem and search algorithms. PTAS: A hybrid search algorithm Experimental results Future work

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Online configuration of large-scale systems such as networks require parameter optimization (e.g. setting link weights) to be done within a limited amount of time. This time limit is even more pressing when configuration is needed as a recovery response to a failure (link failures) in the system.

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Routers flood information to learn topology Determine “next hop” to reach other routers… Compute shortest paths based on link weights Link weights configured by network operator J. Rexford et al.,

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How to set the weights? Inversely proportional to link capacity? Proportional to propagation delay? Network-wide optimization based on traffic? J. Rexford et al.,

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Empirical way: Network administrator experience Trial and error error-prone, not scalable J. Rexford et al.,

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congestion 20

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Which algorithm is better? NFL Theorem(Wolpert, 1997): No matter what perform metric is used, the average performance of any search algorithm will be the same over all possible problems. General-purpose universal algorithm is impossible

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Exploration: global phase, examine overall features, supply effectiveness Exploitation: local phase, examine microscopic features, supply efficiency

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Exploration techniques: Random sampling Random walk Genetic Algorithm Exploitation techniques: Downhill simplex Hillclimbing Simulated Annealing Hybrid Recursive Random Search (RRS), T. Ye et al. ToN 2009

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Exploration techniques: Random sampling Random walk Genetic Algorithm Exploitation techniques: Downhill simplex Hillclimbing Simulated Annealing Hybrid Recursive Random Search (RRS), T. Ye et al. ToN 2009

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An algorithm may be good at one class of problems, but its performance will suffer in the other problems Key Question: How to design an evolutionary hybrid search algorithm? search for the best search Roulette wheel: Punish the bad algorithms and reward the good ones trans-algorithmic Transfer the best-so-far among the algorithms

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The best known strategy to select among slot machines for investment! Viewing each algorithm as a slot machine!

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Total Budget = Round budget = 300 Algorithm-1 Round-1 budget=100 Algorithm-2Algorithm-3 budget=100 Winner Algorithm-1 Round-2 budget=110 Algorithm-2Algorithm-3 budget=98 budget=92 Winner Algorithm-1 Round-3 budget=106 Algorithm-2Algorithm-3 budget=90 budget=104 Winner Algorithm-1 Round-4 budget=120 Algorithm-2Algorithm-3 budget=92 budget=88 Winner Algorithm-1 Round-5 budget=110 Algorithm-2Algorithm-3 budget=102 budget=88 Winner

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We used several benchmark objective functions to model the black-box system: Square Sum function Rastrigin function Griewangk’s Function Axis parallel hyper-ellipsoid function Rotated hyper-ellipsoid function Ackley’s Path function. PTAS outperforms all the other three algorithms for most of the objective functions

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Square Sum function: f1(x)=sum(x(i)^2), i=1:n

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Griewangk's function f(x)=sum(x(i)^2/4000)-prod(cos(x(i)/sqrt(i)))+1, i=1:n

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PTAS’ benefits are more pronounced when objective function changes SquareSum -> Rastrigin -> SquareSum

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PTAS’ benefits are more pronounced when objective function changes Griewangks -> Rastrigin -> Griewangks

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Simulation Setup: Ns-2 Exodus topology from Rocketfuel # of flows: 90 # of nodes: 22 # of links: 37 Confidence interval: 80% (We repeated the optimization process 30 times to gain confidence.) Optimization objective: minimize the overall packet drop rate. Thus, maximize aggregate network throughput

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PTAS NS-2 simulator Aggregated Througput Change link weights

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6% 15% 33%

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PTAS framework is applicable to the various network configuration problems, e.g.: Random Early Detection (RED) queue management algorithm BGP inter-domain traffic engineering

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Thank you…

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