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000151699 02470 $$2ISI$$a000286345400047
000151699 037__ $$aCONF 000151699 245__$$aImproved Constructions for Non-adaptive Threshold Group Testing
000151699 269__ $$a2010 000151699 260__$$bSpringer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa$$c2010 000151699 336__$$aConference Papers
000151699 490__ $$aLecture Notes in Computer Science 000151699 520__$$aThe basic goal in combinatorial group testing is to identify a set of up to d defective items within a large population of size n >> d using a pooling strategy. Namely, the items can be grouped together in pools, and a single measurement would reveal whether there are one or more defectives in the pool. The threshold model is a generalization of this idea where a measurement returns positive if the number of defectives in the pool passes a fixed threshold u, negative if this number is below a fixed lower threshold L <= u, and may behave arbitrarily otherwise.  We study non-adaptive threshold group testing (in a possibly noisy setting)  and show that, for this problem, O(d^{g+2} (\log d)  log(n/d))  measurements (where g := u-L) suffice to identify the defectives, and also present almost matching lower bounds. This significantly improves the previously known non-constructive) upper bound O(d^{u+1} log(n/d)). Moreover, we obtain a framework for   explicit construction of measurement schemes using lossless condensers. The number of measurements resulting from this scheme is ideally bounded by O(d^{g+3} (\log d) \log n).  Using   state-of-the-art constructions of lossless condensers, however, we come up with explicit testing schemes with O(d^{g+3} (\log d) quasipoly(log n)) and O(d^{g+3+beta} poly(log n)) measurements, for arbitrary constant beta > 0.
000151699 6531_ $$aalgo_misc 000151699 700__$$aCheraghchi, Mahdi
000151699 7112_ $$a37th International Colloquium on Automata, Languages and Programming (ICALP)$$cBordeaux, France$$dJuly 5-10, 2010 000151699 773__$$tProceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP)
000151699 909C0 $$0252198$$pALGO$$xU10735 000151699 909CO$$ooai:infoscience.tind.io:151699$$pconf$$pIC
000151699 917Z8 $$x166246 000151699 917Z8$$x166246
000151699 937__ $$aEPFL-CONF-151699 000151699 973__$$aEPFL$$rREVIEWED$$sPUBLISHED
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