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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

References

[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 athttp://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-print available 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

Overview

Mapping network paths to Measurement weights

Key tools: “Almost” Expanders Without Left Regularity

Encoder (Toy Example)

Decoder (Toy Example)

N(V,E) is sufficiently connected.

Network Tomography via Compressive Sensing

Approach: Compressive Sensing. Random walk.

At most k links are in an unknown state (e.g. only a few bottleneck links)

Network path Measurements

Measurement Graph

Network Tomography vs Compressive Sensing

Congested

Construction of Measurement Graph G

Expansion without Left Regularity

Sets of measurements(Co-prime vector)

Local Loops (implemented by source-based routing)

Leaf-based Decoding• Leaf identification (Co-prime

vector)• Localization (Unique signature)

Future Work

Problem:

Process: End-to-end measurement.

Key tools: Coupon Collection Problem

…

Graph: “Hide”or “Utilize”?

Mixing Time:

Key tools: Mixing Time for Random Walk

How many steps before one “gets lost”?

Transition Matrix

Estimate link by link:

How many packets of crisp instant noodles to collect n=108 characters?

: the probability of collecting a new character given i-1 characters.

: the second largest eigenvalue of P.

Complete Graph:

Cycle:

Can we exploit the structure of the graph?

Does not expandExpands

- 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])