Amortized Analysis of Leftist Heaps
| Autor: | Schoenmakers, Berry |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Principles of Verification: Cycling the Probabilistic Landscape, Part I, LNCS 15260, Springer 2024, pp. 73-84 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/978-3-031-75783-9_3 |
| Popis: | Leftist heaps and skew heaps are two well-known data structures for mergeable priority queues. Leftist heaps are constructed for efficiency in the worst-case sense whereas skew heaps are self-adjusting, designed for efficiency in the amortized sense. In this paper, we analyze the amortized complexity of leftist heaps to initiate a full performance comparison with skew heaps. We consider both the leftist heaps originally developed by Crane and Knuth, which are also referred to as rank-biased (or, height-biased) leftist heaps, and the weight-biased leftist heaps introduced by Cho and Sahni. We show how weight-biased leftist heaps satisfy the same exact amortized bounds as skew heaps. With these matching bounds we establish a nice trade-off in which storage of weights is used to limit the worst-case complexity of leftist heaps, without affecting the amortized complexity compared to skew heaps. For rank-biased leftist heaps, we obtain the same amortized lower bounds as for skew heaps, but whether these bounds are tight is left as an open problem. Comment: 13 pages, 3 figures, full version (incl. Appendix B) |
| Databáze: | arXiv |
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