An asymptotic theory for recurrence relations based on minimization and maximization
نویسندگان
چکیده
We derive asymptotic approximations for the sequence f(n) de5ned recursively by f(n) = min16j¡n {f(j) + f(n− j)}+ g(n), when the asymptotic behavior of g(n) is known. Our tools are general enough and applicable to another sequence F(n) = max16j¡n {F(j) + F(n − j) + min{g(j); g(n− j)}}, also frequently encountered in divide-and-conquer problems. Applications of our results to algorithms, group testing, dichotomous search, etc. are discussed. c © 2002 Elsevier Science B.V. All rights reserved. MSC: 68W40; 68Q25; 05A20; 11B37
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عنوان ژورنال:
- Theor. Comput. Sci.
دوره 290 شماره
صفحات -
تاریخ انتشار 2003