Abstract
Let us be given a set of water samples where possibly some are contaminated with a chemical substance. We wish to find these ”defective” samples and their concentrations. Assume that there is an indicator available that can only detect whether the concentration is at least a known threshold, but we may split, merge, and dilute different samples. This problem is a generalized version of the well-known group testing problem and is also related to learning Boolean threshold functions.
First we consider the problem of approximating the concentration in a single sample by a threshold indicator only. We present a practical and efficient strategy that achieves a close approximation using a small number of tests and auxiliary operations. This strategy is formulated as a pebble moving game on a suitable graph.
Then we give principal asymptotic complexity results for finding, in a set of samples, those samples where the concentration exceeds a given limit. The results for the number of tests are asymptotically optimal, furthermore we propose a way for the efficient use of the other resources.
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© 1997 Springer-Verlag Berlin Heidelberg
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Damaschke, P. (1997). The algorithmic complexity of chemical threshold testing. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_73
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DOI: https://doi.org/10.1007/3-540-62592-5_73
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