## Pairing heaps with O(log log n) decrease cost (2009)

Venue: | In 20th ACM-SIAM Symposium on Discrete Algorithms |

Citations: | 5 - 2 self |

### BibTeX

@INPROCEEDINGS{Elmasry09pairingheaps,

author = {Amr Elmasry},

title = {Pairing heaps with O(log log n) decrease cost},

booktitle = {In 20th ACM-SIAM Symposium on Discrete Algorithms},

year = {2009},

pages = {471--476}

}

### OpenURL

### Abstract

We give a variation of the pairing heaps for which the time bounds for all the operations match the lower bound proved by Fredman for a family of similar self-adjusting heaps. Namely, our heap structure requires O(1) for insert and findmin, O(log n) for delete-min, and O(log log n) for decreasekey and meld (all the bounds are in the amortized sense except for find-min). 1

### Citations

373 |
Self-adjusting binary search trees
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- 1985
(Show Context)
Citation Context ...e restrictions governing other structures and the necessity of maintaining structural information, selfadjusting structures showed practical superiority over their counterparts. Following splay trees =-=[12]-=-, a self-adjusting alternative to balanced trees with many other interesting properties, the next move was a self-adjusting heap. Fredman et al. [6] introduced the pairing heaps as a selfadjusting alt... |

138 | Amortized computational complexity - Tarjan - 1985 |

86 |
An empirical comparison of priority-queue and event-set implementations
- Jones
- 1986
(Show Context)
Citation Context ...s buffer are first combined into one tree using the multi-pass pairing, this tree is then linked with the main heap. Despite the inability to prove better bounds for decrease-key, several experiments =-=[8, 9, 13]-=- were conducted illustrating that the pairing heaps are practically superior to other heaps, including the Fibonacci heaps, especially for applications that involve decrease-key operations! Other expe... |

46 |
Self adjusting heaps
- Sleator, Tarjan
- 1986
(Show Context)
Citation Context ...ation were also given [1, 6]. Iacono [7] and Elmasry [2] studied some distribution-sensitive properties of the pairing heaps. Around the same time of introducing the pairing heaps, Sleator and Tarjan =-=[11]-=- also introduced the skew heaps, another self-adjusting heap structure. As first introduced, the skew heaps did not support the decrease-key operation, but can be extended to support it in O(log n) ti... |

40 | An empirical assessment of algorithms for constructing a minimum spanning tree
- Moret, Shapiro
- 1994
(Show Context)
Citation Context ...s buffer are first combined into one tree using the multi-pass pairing, this tree is then linked with the main heap. Despite the inability to prove better bounds for decrease-key, several experiments =-=[8, 9, 13]-=- were conducted illustrating that the pairing heaps are practically superior to other heaps, including the Fibonacci heaps, especially for applications that involve decrease-key operations! Other expe... |

31 |
Pairing heaps: Experiments and analysis
- Stasko, Vitter
- 1987
(Show Context)
Citation Context ...r skew-heap operations are O(log n), still lagging behind those of Fibonacci heaps. 471 Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.One year after, Stasko and Vitter =-=[13]-=- were able to improve the amortized time bound for insert to O(1) by modifying the standard implementation of the pairing heaps using an auxiliary buffer for insertions. With every insertion, a new si... |

20 |
The pairing heap: a new form of self adjusting heap, Algorithmica 1(1
- Fredman, Sedgewick, et al.
- 1986
(Show Context)
Citation Context ...ity over their counterparts. Following splay trees [12], a self-adjusting alternative to balanced trees with many other interesting properties, the next move was a self-adjusting heap. Fredman et al. =-=[6]-=- introduced the pairing heaps as a selfadjusting alternative to Fibonacci heaps. Despite the ingenuity of their structure and proofs, they were able to illustrate an amortized O(log n) bound for vario... |

17 | Improved upper bounds for pairing heaps - Iacono - 2000 |

14 |
On the efficiency of pairing heaps and related data structures
- Fredman
- 1999
(Show Context)
Citation Context ...cted with an attempt to construct a worst-case scenario for the decrease-key operation, but the outcome was that decrease-key takes a constant time in practice! An important step was taken by Fredman =-=[5]-=-, when he showed that a constant amortized cost of decreasekey is precluded by establishing a lower bound of Ω(log log n) for a family of heap structures that generalize the standard implementation of... |

10 | Towards a final analysis of pairing heaps
- Pettie
- 2006
(Show Context)
Citation Context ...lies a constant cost for the decrease-key operation when m = Ω(n 1+ǫ ), for any constant ǫ > 0. The gap between the upper bound and the lower bound for decrease-key lasted for six years, until Pettie =-=[10]-=- proved an O(2 2√ log log n ) upper bound, the first sublogarithmic bound for operations other than delete-min. He also conjectured that Fredman’s lower bound is tight. In this paper, we give a variat... |

5 |
Parametrized self-adjusting heaps
- Elmasry
(Show Context)
Citation Context ...a single tree remains. The O(log n) bound does not apply for the multi-pass variant of the pairing heaps. Other variants with different linking strategies for the delete-min operation were also given =-=[1, 6]-=-. Iacono [7] and Elmasry [2] studied some distribution-sensitive properties of the pairing heaps. Around the same time of introducing the pairing heaps, Sleator and Tarjan [11] also introduced the ske... |

3 |
Adaptive properties of pairing heaps
- Elmasry
- 2001
(Show Context)
Citation Context ...g n) bound does not apply for the multi-pass variant of the pairing heaps. Other variants with different linking strategies for the delete-min operation were also given [1, 6]. Iacono [7] and Elmasry =-=[2]-=- studied some distribution-sensitive properties of the pairing heaps. Around the same time of introducing the pairing heaps, Sleator and Tarjan [11] also introduced the skew heaps, another self-adjust... |

3 |
A priority queue transform
- Fredman
- 1999
(Show Context)
Citation Context ...s therefore not asymptotically as efficient as Fibonacci heaps. Left with skew heaps, one would think about the possibility of improving the bound for decrease-key. This was also precluded by Fredman =-=[4]-=- who introduced a transformation, referred to as depletion, which when applied to skew heaps induces the skew-pairing heaps. This implies that his lower bound, as applying to skewpairing heaps, also a... |

1 |
Unpublished experiments
- Elmasry, Fredman
- 1997
(Show Context)
Citation Context ...nducted illustrating that the pairing heaps are practically superior to other heaps, including the Fibonacci heaps, especially for applications that involve decrease-key operations! Other experiments =-=[3]-=- were also conducted with an attempt to construct a worst-case scenario for the decrease-key operation, but the outcome was that decrease-key takes a constant time in practice! An important step was t... |