Recurrence Relations

Abstract

This chapter introduces this important tool used in analysis of algorithms. It starts by the formal definition of recurrence relations and discussed their classification into homogeneous and non-homogeneous and by order. It introduces the idea of a solution, of solution verification and guessing. The following sections provide a few theorems that help solving recurrence relations, followed by systematic procedures to solve first homogeneous recurrence relations, then non-homogeneous with polynomial and exponential terms. Another section is dedicated to recurrence relations involving the floor and ceiling functions. The last section surveys methods for solving recurrence relations that do not fit the previous categories and also provides a theorem for finding an upper bound of the solution.