Combinatorial Search Problems: Lectures held at the by Gyula Katona

By Gyula Katona

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Extra resources for Combinatorial Search Problems: Lectures held at the Department for Automation and Information June 1972

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The maximal number of r-wise qualitative ig dependent sets is not determined yet. An estimation is given in Renyi 1 s book (1971). Exac_! ', of the elements of X'= (x:, ... , X~n} is "defective" (it is the subset of all defective elements). However, the testing subsets A eX are also transformed . A has a defective element with the set x'~ of defective elements. t-A' where A' is the set of xk non-disjoin t to xJ • However, such subsets A' are very special, we reduced our problem to a problem of type (Aoc )(Boc)(Cj) )(D ex, )(Ecx,) Indipendently infected elements 37 The restrictions for the testing subsets are very particular.

27) 1. } + {tog 3} ... ) + n - 3. Steinhaus conjectured in (1950) this procedure to be optimal, ho~ ever in (1958) he disproved the conjecture. 27)) bounds are equivalent, but we do not know the best algorithm up to now. Ford and johnson (1959) determined an algorithm better than Steinhaus's one. (See also Wells (1965), and Cesari (1968)). A generalization of the above problem is to find and order the t largest y's. This generalization does not belong to the general search problem treated here.

Amer. Math. Monthly, 70, 136-148. L. (1968): Note on the connection between search the ory and coQing theory, Proc. of the Collog. on Information Theory, ed. by A. Renyi, janos Bolyai Math. , Budapest Hungary. G. (1964): Determining a set from the cardinalities of its intersections with other sets. Canad. ]. , 16' 94-97. , Y. (1968): Questionnaire, codage et tris, Institute Blaise Pascal, Paris. (1970): Optimisation des questionnaires avec contrain te de rang. Z. : On the Enumeration of PseudoSearch Codes.

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