The analysis of algorithms
Introduction to algorithms
A general method for solving divide-and-conquer recurrences
ACM SIGACT News
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A real elementary approach to the master recurrence and generalizations
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
A master theorem for discrete divide and conquer recurrences
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A Master Theorem for Discrete Divide and Conquer Recurrences
Journal of the ACM (JACM)
A new dichotomic algorithm for the uniform random generation of words in regular languages
Theoretical Computer Science
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In this article, we present a general solution for linear divide-and-conquer recurrences of the form\[u_n=\sum_{i=1}^{k} a_iu_{\lfloor \frac{n}{b_i} \rfloor} + g(n).\]Our approach handles more cases than the Master method does\cite{Bently}. We achievethis advantage by defining a new transform - the Order transform - which hasuseful properties for providing asymptotic answers (compared to other transformswhich supply exact answers). This transform helps in mapping the sequence under considerationto the two dimensional plane where the solution becomes easier to obtain. Wedemonstrate the power of the final results by solving many ’’difficult" examples.