Akra–Bazzi method

The Akra–Bazzi method is a theorem-based technique for deriving asymptotic bounds on divide-and-conquer recurrences with unequal subproblem sizes and additive costs.

Akra–Bazzi theorem: A theorem giving asymptotic bounds for recurrences with multiple scaled subproblems and a regular additive cost. It formalizes the method’s conditions and the formula used to obtain the solution.
Divide-and-conquer algorithm: An algorithmic strategy that divides a problem into smaller subproblems, solves them recursively, and combines their results. The method analyzes the running-time recurrences produced by this strategy.
Unequal-subproblem recurrence: A recurrence whose recursive terms use different constant fractions of the original input. This is the central recurrence shape addressed by the method.
Master theorem: A theorem for asymptotic solutions to recurrences with equal-sized recursive subproblems and regular additive work. Akra–Bazzi extends the analysis to multiple subproblem sizes.
Mohamad Akra: A mathematician who coauthored the theorem underlying the Akra–Bazzi method. His name forms the first half of the theorem’s standard attribution.
Characteristic exponent: The real number p satisfying the balance equation ∑ aᵢbᵢᵖ = 1 for a divide-and-conquer recurrence. It identifies the power-law contribution from the recursive branches.
Recurrence relation: An equation defining a function using values of that function at smaller inputs. Akra–Bazzi applies to a structured family of such equations.
Binary search: A search algorithm that repeatedly halves a sorted search interval. Its recurrence is a simple special case with one recursive subproblem.
Recursion tree method: A technique that estimates recurrence solutions by summing work across levels of a recursion tree. It offers an intuitive derivation, while Akra–Bazzi packages the result in a theorem.
L. M. Bazzi: A mathematician who coauthored the theorem underlying the Akra–Bazzi method. His name forms the second half of the theorem’s standard attribution.

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