Finding a Divisible Pair and a Good Wooden Fence
نویسندگان
چکیده
We consider two algorithmic problems arising in the lives of Yogi Bear and Ranger Smith. The first problem is the natural algorithmic version of a classic mathematical result: any (n + 1)subset of {1, . . . , 2n} contains a pair of divisible numbers. How do we actually find such a pair? If the subset is given in the form of a bit vector, we give a RAM algorithm with an optimal running time of O(n/ lg n). If the subset is accessible only through a membership oracle, we show a lower bound of 4 3 n−O(1) and an almost matching upper bound of ` 4
منابع مشابه
Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...
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