By Ding-Zhu Du, Frank Kwang Hwang

ISBN-10: 9810241070

ISBN-13: 9789810241070

Crew checking out has been utilized in scientific, chemical and electric checking out, coding, drug screening, toxins regulate, multiaccess channel administration, and extra lately in facts verification, clone library screening and AIDS checking out. The mathematical version will be both combinatorial or probabilistic. This paintings is a precis of all vital effects lower than the combinatorial version, and it demonstrates their functions in actual difficulties. another seek difficulties, together with the well-known counterfeit-coins challenge, also are studied extensive. This moment variation is up-to-date and embraces the turning out to be significance of 2 subject matters: nonadaptive algorithms and blunder tolerance. new chapters, one on clone library screening and the opposite on errors tolerance, were extra. 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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**Extra info for Combinatorial Group Testing and Its Applications**

**Example text**

Denote the new problem by yn x n. 4 M(Th x n) = Ilogmnl for all m and n. , A and B are ordered sets and a test group must consist of items from the top of the two orders. He showed that for m = 11 and n = (2101 - 1)/11 (which is an integer by Fermat's theorem), the first test group must consist of 8 items from A and 2101-4 items from B. 8, then [log mnJ suffice. Weng and Hwang [14] considered the case of k disjoint sets. ,m. XSm)=2m+1 Proof. Since 2 m + 1 _1 nm 0 (22' + 1) = 2 22m +1 M(S0 x S, x ...

2 7r is realizable if and only if G,r does not contain a directed cycle. Proof. Suppose G, has a cycle C. Let 7r' be a partition of So obtained by merging two (separable) sets Si and Si in 7r. 1, G, cannot contain the cycle Si -+ Si -* Si for otherwise Si and Si are not separable , therefore not mergeable. Since every edge in G, except those between Si and Si is preserved in G,r', G,, must 22 General Sequential Algorithms contain a cycle C. By repeating this argument , eventually one obtains a partition with no two parts separable .

5). 7 Number of Group Testing Algorithms One interesting problem is to count the number of group testing algorithms for S. This is the total number of binary trees with ISI leaves (labeled by members of S) which satisfy the group testing structure . While this problem remains open, Moon and Sobel [13] counted for a class of algorithms when the sample space S is the power set of n items. Call a group pure if it contains no defective, and contaminated otherwise. A group testing algorithm is nested if whenever a contaminated group is known , the next group to be tested must be a proper subset of the contaminated group .

### Combinatorial Group Testing and Its Applications by Ding-Zhu Du, Frank Kwang Hwang

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