By Ding-Zhu Du, Frank Kwang Hwang

Staff checking out has been utilized in scientific, chemical and electric checking out, coding, drug screening, toxins keep an eye on, multiaccess channel administration, and extra lately in info verification, clone library screening and AIDS checking out. The mathematical version might be both combinatorial or probabilistic. This paintings is a precis of all very important effects lower than the combinatorial version, and it demonstrates their purposes in genuine difficulties. another seek difficulties, together with the recognized counterfeit-coins challenge, also are studied extensive. This moment version is up-to-date and embraces the starting to be value of 2 issues: nonadaptive algorithms and mistake tolerance. new chapters, one on clone library screening and the opposite on errors tolerance, were additional. additionally integrated is a brand new bankruptcy on counterfeit cash, and the chapters were reorganized into components to supply focuses and views.

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5 If n > 1, then 3 2n-. 5. 526753 . . ; in particular, F(n) > 4az" for n > 1. The proof of this is omitted. References [1] X. M. Chang, F. K. Hwang and J. F. Weng, Group testing with two and three defectives, Ann. N. Y. Acad. Sci. Vol. 576, Ed. M. F. Capobianco, M. Guan, D. F. Hsu and F. Tian, (New York, 1989) 86-96. [2] R. Dorfman, The detection of defective members of large populations, Ann. Math. Statist. 14 (1943) 436-440. [3] M. C. Hu, F. K. Hwang and J. K. Wang, A boundary problem for group testing, SIAM J.

F. Capobianco, M. Guan, D. F. Hsu and F. Tian, (New York, 1989) 86-96. [2] R. Dorfman, The detection of defective members of large populations, Ann. Math. Statist. 14 (1943) 436-440. [3] M. C. Hu, F. K. Hwang and J. K. Wang, A boundary problem for group testing, SIAM J. AIg. Disc. Methods 2 (1981) 81-87. [4] F. K. Hwang, A minimax procedure on group testing problems, Tamkang J. Math. 2 (1971) 39-44. [5] F. K. Hwang, Hypergeometric group testing procedures and merging procedures, Bull. Inst. Math.

1, S -a S1 --^ S implies n S1 = S n {D1} # 0. This implies D1 E S n So. Since D1 ¢ S, S n So S. (iii) = (i): Trivially true by using the definition of realizability. 3 Li ' s s-Stage Algorithm Li [12] extended a 2-stage algorithm of Dorfman [2] (for PGT) to s stages . At stage 1 the n items are arbitrarily divided into gl groups of k, ( some possibly k, - 1) items. Each of these groups is tested and items in pure groups are identified as good and removed. Items in contaminated groups are pooled together and arbitrarily redivided into g2 groups of k2 (some possibly k2 - 1) items; thus entering stage 2.