Multiple-Size Divide-and-Conquer Recurrences

TL;DR

This paper introduces a master theorem that provides tight asymptotic solutions for complex divide-and-conquer recurrences involving multiple recursive terms, extending classical methods to more intricate recurrence relations.

Contribution

It presents a novel master theorem specifically designed for recurrences with multiple recursive calls, broadening the analytical tools available for divide-and-conquer algorithms.

Findings

Provides a formula for tight asymptotic bounds of complex recurrences.

Extends classical master theorem to multiple recursive terms.

Enables precise analysis of more intricate divide-and-conquer algorithms.

Abstract

This short note reports a master theorem on tight asymptotic solutions to divide-and-conquer recurrences with more than one recursive term: for example, T(n) = 1/4 T(n/16) + 1/3 T(3n/5) + 4 T(n/100) + 10 T(n/300) + n^2.