Master theorem - Wikipedia

Master theorem - Wikipedia - Master theorem - Wikipedia,...

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Master theorem From Wikipedia, the free encyclopedia In the analysis of algorithms, the master theorem , which is a specific case of the Akra-Bazzi theorem, provides a cookbook solution in asymptotic terms for recurrence relations of types that occur in practice. It was popularized by the canonical algorithms textbook Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein, which introduces and proves it in sections 4.3 and 4.4, respectively. Nevertheless, not all recurrence relations can be solved with the use of the master theorem. Contents 1 Generic form 2 Case 1 2.1 Generic form 2.2 Example 3 Case 2 3.1 Generic form 3.2 Example 4 Case 3 4.1 Generic form 4.2 Example 5 Inadmissible [1] 6 See also 7 References 8 External links Generic form The master theorem concerns recurrence relations of the form: In the application to the analysis of a recursive algorithm, the constants and function take on the following significance: n is the size of the problem. a is the number of subproblems in the recursion. n / b is the size of each subproblem. (Here it is assumed that all subproblems are essentially the same size.) f ( n ) is the cost of the work done outside the recursive calls, which includes the cost of dividing the problem and the cost of merging the solutions to the subproblems. It is possible to determine an asymptotic tight bound in these three cases:
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This note was uploaded on 01/24/2011 for the course CS 570 at USC.

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Master theorem - Wikipedia - Master theorem - Wikipedia,...

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