Threshold Group Testing
We introduce a natural generalization of the well-studied group testing problem: A test gives a positive (negative) answer if the pool contains at least u (at most l) positive elements, and an arbitrary answer if the number of positive elements is between these fixed thresholds l and u. We show that the p positive elements can be determined up to a constant number of misclassifications, bounded by the gap between the thresholds. This is in a sense the best possible result. Then we study the number of tests needed to achieve this goal if n elements are given. If the gap is zero, the complexity is, similarly to classical group testing, O(plogn) for any fixed u. For the general case we propose a two-phase strategy consisting of a Distill and a Compress phase. We obtain some tradeoffs between classification accuracy and the number of tests.
KeywordsGroup Testing Boolean Function Positive Element Test Complexity Threshold Group
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- 1.Alon, N., Guruswami, V., Kaufman, T., Sudan, M.: Guessing secrets efficiently via list decoding. In: 13th SODA, pp. 254–262 (2002)Google Scholar
- 4.Damaschke, P.: The algorithmic complexity of chemical threshold testing. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds.) CIAC 1997. LNCS, vol. 1203, pp. 205–216. Springer, Heidelberg (1997)Google Scholar
- 12.Ngo, H.Q., Du, D.Z.: A survey on combinatorial group testing algorithms with applications to DNA library screening. DIMACS Series Discrete Math. and Theor. Computer Science, vol. 55, pp. 171–182. AMS (2000)Google Scholar