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

Authors:
Wei-Mei Chen;Gen-Huey Chen
Affiliations:
Department of Applied Mathematics, Tatung University, Taipei, Taiwan;Department of Computer Science & Information Engineering, National Taiwan University, # 1 Roosevelt Rd. Sec. 4, Taipei, Taiwan
Venue:
Theoretical Computer Science - Algorithms,automata, complexity and games
Year:
2003

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Abstract

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.