Divide-and-conquer recurrences associated with generalized heaps, optimal merge, and related structures

An elementary approach is given to studying the recurrence relations associated with generalized heaps (or d-heaps), cost of optimal merge, and generalized divide-and-conquer minimization problems. We derive exact formulae for the solutions of all such recurrences and give some applications. In particular, we present a precise probabilistic analysis of Floyd’s algorithm for constructing d-heaps when the input is randomly given. A variant of d-heap having some interesting combinatorial properties is also introduced.