On optimal randomized group testing with one defective item and a constrained number of positive responses

Dorfman, 1943, The detection of defective members of large populations, Ann. Math. Stat., 14, 436, 10.1214/aoms/1177731363 Sobel, 1959, Group testing to eliminate efficiently all defectives in a binomial sample, Bell Syst. Tech. J., 38, 1179, 10.1002/j.1538-7305.1959.tb03914.x Wolf, 1985, Born again group testing: Multiaccess communications, IEEE Trans. Inform. Theory, IT-31, 185, 10.1109/TIT.1985.1057026 De Bonis, 2003, Constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels, Theoret. Comput. Sci., 306, 223, 10.1016/S0304-3975(03)00281-0 Wein, 1996, Pooled testing for HIV screening: capturing the dilution effect, Oper. Res., 44, 543, 10.1287/opre.44.4.543 Zenios, 1998, Pooled testing for HIV prevalence estimation: exploiting the dilution effect, Stat. Med., 17, 1447, 10.1002/(SICI)1097-0258(19980715)17:13<1447::AID-SIM862>3.0.CO;2-K Hong, 2002, Group testing for image compression, IEEE Trans. Image Process., 11, 901, 10.1109/TIP.2002.801124 N.J.A. Harvey, M. Patrascu, Y. Wen, S. Yekhanin, V.W.S. Chan, Non-Adaptive fault diagnosis for all-optical networks via combinatorial group testing on graphs, in: The 26th IEEE International Conference on Computer Communications, 2007, pp. 697–705. Thai, 2012 C. Lo, M. Liu, J.P. Lynch, A.C. Gilbert, Efficient sensor fault detection using combinatorial group testing, in: 2013 IEEE International Conference on Distributed Computing in Sensor Systems, 2013, pp. 199–206. Du, 2000 Damaschke, 1998, Randomized group testing for mutually obscuring defectives, Inform. Process. Lett., 67, 131, 10.1016/S0020-0190(98)00096-9 De Bonis, 2006, Optimal algorithms for two group testing problems and new bounds on generalized superimposed codes, IEEE Trans. Inform. Theory, 52, 4673, 10.1109/TIT.2006.881740 Cicalese, 2005, Optimal group testing strategies with interval queries and their application to splice site detection, Int. J. Bioinform. Res. Appl., 1, 363, 10.1504/IJBRA.2005.008441 Cicalese, 2007, Overlaps help: Improved bounds for group testing with interval queries, Discrete Appl. Math., 155, 288, 10.1016/j.dam.2006.07.002 Bar-Lev, 2007, Applications of bulk queues to group testing models with incomplete identification, European J. Oper. Res., 183, 226, 10.1016/j.ejor.2006.09.086 Wang, 2007, Non-unique probe selection and group testing, Theoret. Comput. Sci., 381, 29, 10.1016/j.tcs.2007.02.067 Claeys, 2010, A queueing model for general group screening policies and dynamic item arrivals, European J. Oper. Res., 207, 827, 10.1016/j.ejor.2010.05.042 Chen, 2011, An almost optimal algorithm for generalized threshold group testing with inhibitors, J. Comput. Biol., 18, 851, 10.1089/cmb.2010.0030 Ahlswede, 2013, vol. 7777, 488 Chin, 2013, Non-adaptive complex group testing with multiple positive sets, Theoret. Comput. Sci., 505, 11, 10.1016/j.tcs.2013.04.011 Damaschke, 2013, Two new perspectives on multi-stage group testing, Algorithmica, 67, 324, 10.1007/s00453-013-9781-4 A. De Bonis, Efficient group testing algorithms with a constrained number of positive responses, in: Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications, COCOA, 2014, pp. 506–521. De Bonis, 2016, Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing, J. Comb. Optim., 32, 1254, 10.1007/s10878-015-9949-8 Damaschke, 2016, Adaptive group testing with a constrained number of positive responses improved, Discrete Appl. Math., 205, 208, 10.1016/j.dam.2016.01.010 Thomas, 1973, Application of group testing procedures in radiological health, Health Phys., 25, 259, 10.1097/00004032-197309000-00004 Pasternack, 1975, Group-sequential leak-testing of sealed radium sources, Technometrics, 18, 59, 10.2307/1267917 Li, 1962, A sequential method for screening experimental variables, J. Amer. Statist. Assoc., 57, 455, 10.1080/01621459.1962.10480672 A.C. Yao, Probabilistic computations: Toward a unified measure of complexity, in: Proceedings of the 18th IEEE Symposium on Foundations of Computer Science, FOCS, 1977, pp. 222–227. Motwani, 1995 Aigner, 1988