## Abstract On the Power of Structural Violations in Priority Queues

Citations: | 1 - 0 self |

### BibTeX

@MISC{Elmasry_abstracton,

author = {Amr Elmasry and Claus Jensen and Jyrki Katajainen},

title = {Abstract On the Power of Structural Violations in Priority Queues},

year = {}

}

### OpenURL

### Abstract

We give a priority queue that guarantees the worstcase cost of Θ(1) per minimum finding, insertion, and decrease; and the worst-case cost of Θ(lg n) with at most lg n + O ( √ lg n) element comparisons per deletion. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and lg n is a shorthand for max {1,log 2 n}. In contrast to a run-relaxed heap, which allows heaporder violations, our priority queue relies on structural violations. By mimicking a priority queue that allows heap-order violations with one that only allows structural violations, we improve the bound on the number of element comparisons per deletion to lg n + O(lg lg n).

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Citation Context ...order violation means that a node stores an element that is smaller than the element stored at its parent. A separate structure is maintained to keep track of all such violations. In Fibonacci heaps (=-=Fredman & Tarjan 1987-=-) and thin heaps (Kaplan & Tarjan 1999) structural violations are allowed. A structural violation means that a node has lost one or more of its subtrees. Kaplan & Tarjan Partially supported by the Dan... |

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Citation Context ...here Φ is the golden ratio. This bound can be reduced to log Φ n + O(lg lg n) using the twotier framework described in (Elmasry 2004, Elmasry et al. 2004) (log Φ n ≈ 1.44lg n). For run-relaxed heaps (=-=Driscoll et al. 1988-=-) this bound is 3lg n+O(1) in the worst case [as analysed in (Elmasry et al. 2004, Elmasry et al. 2006)], and the bound can be improved to lg n + O(lg lg n) using the two-tier framework (Elmasry et al... |

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Citation Context ...delete-min and delete is 2log Φ n + O(1) in the amortized sense, where Φ is the golden ratio. This bound can be reduced to log Φ n + O(lg lg n) using the twotier framework described in (Elmasry 2004, =-=Elmasry et al. 2004-=-) (log Φ n ≈ 1.44lg n). For run-relaxed heaps (Driscoll et al. 1988) this bound is 3lg n+O(1) in the worst case [as analysed in (Elmasry et al. 2004, Elmasry et al. 2006)], and the bound can be improv... |

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