FRANTIC A Fast Referencebased Algorithm for Network Tomography

FRANTIC: A Fast Reference-based Algorithm for Network Tomography via Compressive Sensing Sheng Cai, Mayank Bakshi, Sidharth Jaggi, Minghua Chen Overview Network Tomography via Compressive Sensing Problem: Key tools: Coupon Collection Problem Encoder (Toy Example) How many packets of crisp instant noodles to collect n=108 characters? 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 Weights are constrained to be integers Choice of weights is constrained by network topology Can Efficient Compressive Sensing Algorithms help? (e. g. [1]) TEMPLATE DESIGN © 2008 www. Poster. Presentations. co m Expands Does not expand [1] Sheng Cai, Mayank Bakshi, 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/~cs 010/files/Infocom 13. 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-print available at http: //personal. ie. cuhk. edu. hk/~sjaggi/CS_)1. pdf, Video at http: //youtu. be/Ur. Ts. ZX 7 -fh. I [3] Weiyu Xu; Mallada, E. ; Ao Tang; , "Compressive sensing over graphs, " INFOCOM, 2011