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Efficient Noisy Group Testing: Adaptive vs. Non-Adaptive Strategies for Optimal Testing

This work explores the comparison between adaptive and non-adaptive group testing methods in the context of noisy measurements. Leveraging findings from the 49th Annual Allerton Conference, we present near-optimal bounds and efficient algorithms for both testing strategies. The paper discusses the lower bounds of the number of tests required and outlines a two-stage adaptive approach. We delve into the complexities of decoding, highlighting innovations in probabilistic group testing. The implications for practical applications in communication and computing systems are also considered.

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Efficient Noisy Group Testing: Adaptive vs. Non-Adaptive Strategies for Optimal Testing

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  1. Noisy Group Testing (Quick and Efficient) • ShengCai, MayankBakshi, SidharthJaggi The Chinese University of Hong Kong • Mohammad Jahangoshahi • Sharif University of Technology

  2. q q Group Testing Adaptive vs. Non-adaptive What’s known [CCJS11] For Pr(error)< ε , Lower bound of number of tests: Chun Lam Chan; Pak HouChe; Jaggi, S.; Saligrama, V.; , "Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms,"  49th Annual Allerton Conference on Communication, Control, and Computing, pp.1832-1839, 28-30 Sept. 2011 [CCJS11]

  3. This work # Tests Adaptive  Non-Adaptive  Lower bound Two-Stage Adaptive  [NPR12]  O(poly(D)log(N)),O(D2log(N))  O(DN),O(Dlog(N))   O(Dlog(N))  Lower bound Decoding complexity O(Dlog(N))

  4. Hammer: GROTESQUE Testing

  5. Hammer: GROTESQUE Testing

  6. Hammer: GROTESQUE Testing

  7. Hammer: GROTESQUE Testing

  8. Testing Matrix IN OUT Negative 0 Positive 1

  9. Multiplicity ?

  10. Multiplicity (d = 0)

  11. Multiplicity (d = 0)

  12. Multiplicity (d = 0)

  13. Multiplicity (d = 0) d = 0 No positive tests

  14. Multiplicity (d = 1)

  15. Multiplicity (d = 1)

  16. Multiplicity (d = 1)

  17. Multiplicity (d = 1) d = 1 50% positive tests

  18. Multiplicity (d = 2)

  19. Multiplicity (d = 2)

  20. Multiplicity (d = 2)

  21. Multiplicity (d = 2) d = 2 75% positive tests Statistical Difference!

  22. Multiplicity ?

  23. Localization ?

  24. Localization Signature Test Outcome BSC (q) Channel Expander Codes Decoder Particular Signature

  25. Hammer: GROTESQUE Testing

  26. Nail: “Good” Partioning N items D defectives

  27. Adaptive Group Testing Groups

  28. Adaptive Group Testing Groups Decaying geometrically Tests

  29. Adaptive Group Testing The number of unidentified defectives <

  30. Adaptive Group Testing Tests of size Coupon Collection

  31. Non-Adaptive Group Testing Groups constant fraction of “Good” groups Tests

  32. Non-Adaptive Group Testing

  33. Non-Adaptive Group Testing Independent partitions Coupon Collection Tests

  34. 2-Stage Adaptive Group Testing Groups (Birthdays)

  35. 2-Stage Adaptive Group Testing Non-adaptive Group Testing + Tests

  36. Summary of this work # Tests    O(Dlog(N)) Decoding complexity O(Dlog(N))

  37. Thank you謝謝

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