An asymptotic theory for recurrence relations based on minimization and maximization
Theoretical Computer Science
Theoretical Computer Science
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Bounds are obtained for the solution to the divide-and-conquer recurrence \[M(n) = \max_{k_1 + \cdots + k_p = n} (M(k_1) + M(k_2) +\cdots + M(k_p) + \min (f(k_1), \cdots, f(k_p))),\] for nondecreasing functions $f$. Similar bounds are found for the recurrence with "min" replaced by "sum-of-all-but-the-max." Such recurrences appear in the analysis of various algorithms. The bounds follow from analyses of partition trees.