Noise-resilient group testing: Limitations and constructions

  • Authors:

  • Mahdi Cheraghchi

  • Affiliations:

  • -

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2013

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Abstract

We study combinatorial group testing schemes for learning d-sparse Boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that any noise-resilient scheme in this model can only approximately reconstruct the sparse vector. On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of @W@?(d^2logn) that is known for exact reconstruction of d-sparse vectors of length n via non-adaptive measurements, by a multiplicative factor @W@?(d). Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with m=O(dlogn) measurements, that allow efficient reconstruction ofd-sparse vectors up to O(d) false positives even in the presence of @dm false positives and O(m/d) false negatives within the measurement outcomes, for any constant @d