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Goal : Quickly infer the link delays from few measurement.

FRANTIC: A Fast Reference-based Algorithm for Network Tomography via Compressive Sensing Sheng Cai , Mayank Bakshi , Sidharth Jaggi, Minghua Chen. Overview. Key tools: Coupon Collection Problem. Encoder (Toy Example).

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Goal : Quickly infer the link delays from few measurement.

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  1. FRANTIC: A Fast Reference-based Algorithm for Network Tomography via Compressive Sensing Sheng Cai, MayankBakshi, Sidharth Jaggi, Minghua Chen Overview Key tools: Coupon Collection Problem Encoder (Toy Example) • How many packets of crisp instant noodles to collect n=108 characters? • Network Tomography via Compressive Sensing • Problem: • At most k links are in an unknown state(e.g. only a few bottleneck links) • Sets of measurements • (Co-prime vector) • Congested • Local Loops (implemented • by source-based routing) • N(V,E) is sufficiently connected. • : the probability of collecting a new • character given i-1 characters. Key tools: Mixing Time for Random Walk • Process: End-to-end measurement. • How many steps before one “gets lost”? Decoder (Toy Example) • Goal: Quickly infer the link delays from few measurement. • … • Leaf-based Decoding • Leaf identification (Co-prime vector) • Localization (Unique signature) • Approach: Compressive Sensing. • Random walk. • Transition Matrix • Mixing Time: Mapping network paths to Measurement weights • : the second largest eigenvalue of P. • Network path • Measurements Key tools: “Almost” Expanders Without Left Regularity Future Work • Graph: “Hide”or “Utilize”? • Construction of Measurement Graph G • Complete Graph: • Cycle: • Estimate link by link: • Expansion without Left Regularity • Measurement Graph • Can we exploit the structure of the graph? • Network Tomography vs Compressive Sensing References • Measurement output = weighted linear combination of the input vector • Input vector is sparse [1] Sheng Cai, MayankBakshi, Sidharth Jaggi, Minghua Chen, “A Better TOMORROW: A Fast Algorithm for Network Tomography with Few Probes”, in preparation. Early versiion available at http://personal.ie.cuhk.edu.hk/~cs010/files/Infocom13.pdf. [2] M. Bakshi, S. Jaggi, S. Cai, M. Chen, “Order-optimal compressive sensing for k-sparse signals with noisy tails: O(k) measurements, O(k) steps”, pre-printavailable at http://personal.ie.cuhk.edu.hk/~sjaggi/CS_)1.pdf, Video at http://youtu.be/UrTsZX7-fhI [3] Weiyu Xu; Mallada, E.; Ao Tang; , "Compressive sensing over graphs," INFOCOM, 2011 • Weights are constrained to be integers • Choice of weights is constrained by network topology • Does not expand • Expands • Can Efficient Compressive Sensing Algorithms help? (e.g. [1])

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