An average case analysis of Floyd's algorithm to construct heaps
Information and Control
SIAM Journal on Computing
Finding the median requires 2n comparisons
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Journal of Algorithms
On the complexity of partial order productions
SIAM Journal on Computing
The information theory bound is tight for selection in a heap
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Communications of the ACM
WG '80 Proceedings of the International Workshop on Graphtheoretic Concepts in Computer Science
An efficient algorithm for partial order production
Proceedings of the forty-first annual ACM symposium on Theory of computing
An Efficient Algorithm for Partial Order Production
SIAM Journal on Computing
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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In this paper, we investigate the complexity of heaps. In particular, we study the construction problem and the search problem for heaps. We derive an adversary-based lower bound for the heap construction problem. It is shown that 1.5(n + 1)–log(n + 1)–2 comparisons are necessary to construct a heap of size n in the worst case. This is the first non-trivial adversary lower bound for this problem, which improves the previous best lower bound based on an information theoretical argument for the heap construction. Furthermore, we prove fairly trivial tight upper and lower bounds on the number of comparisons needed to search for a given element in a heap. An optimal 3/4n-time search algorithm is presented. Our lower bound for searching is also demonstrated by an adversary argument, which improves the information theory bound for the problem as well.