### Abstract

A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Ω(log log n/log log log n) amortized time on the Decrease-Key operation (given O(logn) amortized-time Extract-Min). Intuitively, this bound shows the key to having O(1)-time Decrease-Key is the ability to sort O(logn) items in O(logn) time; Fibonacci heaps [M. .L. Fredman and R. E. Tarjan. J. ACM 34(3):596-615 (1987)] do this through the use of bucket sort. Our lower bound also holds no matter how much data is augmented; this is in contrast to the lower bound of Fredman [J. ACM 46(4):473-501 (1999)] who showed a tradeoff between the number of augmented bits and the amortized cost of Decrease-Key. A new heap data structure, the sort heap, is presented. This heap is a simplification of the heap of Elmasry [SODA 2009: 471-476] and shares with it a O(loglogn) amortized-time Decrease-Key, but with a straightforward implementation such that our lower bound holds. Thus a natural model is presented for a pointer-based heap such that the amortized runtime of a self-adjusting structure and amortized lower asymptotic bounds for Decrease-Key differ by but a O(logloglogn) factor.

Original language | English (US) |
---|---|

Title of host publication | Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings |

Publisher | Springer Verlag |

Pages | 637-649 |

Number of pages | 13 |

Volume | 8572 LNCS |

Edition | PART 1 |

ISBN (Print) | 9783662439470 |

DOIs | |

State | Published - 2014 |

Event | 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark Duration: Jul 8 2014 → Jul 11 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Number | PART 1 |

Volume | 8572 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 |
---|---|

Country | Denmark |

City | Copenhagen |

Period | 7/8/14 → 7/11/14 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings*(PART 1 ed., Vol. 8572 LNCS, pp. 637-649). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8572 LNCS, No. PART 1). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_53

**Why some heaps support constant-amortized-time decrease-key operations, and others do not.** / Iacono, John; Özkan, Özgür.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings.*PART 1 edn, vol. 8572 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 8572 LNCS, Springer Verlag, pp. 637-649, 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014, Copenhagen, Denmark, 7/8/14. https://doi.org/10.1007/978-3-662-43948-7_53

}

TY - GEN

T1 - Why some heaps support constant-amortized-time decrease-key operations, and others do not

AU - Iacono, John

AU - Özkan, Özgür

PY - 2014

Y1 - 2014

N2 - A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Ω(log log n/log log log n) amortized time on the Decrease-Key operation (given O(logn) amortized-time Extract-Min). Intuitively, this bound shows the key to having O(1)-time Decrease-Key is the ability to sort O(logn) items in O(logn) time; Fibonacci heaps [M. .L. Fredman and R. E. Tarjan. J. ACM 34(3):596-615 (1987)] do this through the use of bucket sort. Our lower bound also holds no matter how much data is augmented; this is in contrast to the lower bound of Fredman [J. ACM 46(4):473-501 (1999)] who showed a tradeoff between the number of augmented bits and the amortized cost of Decrease-Key. A new heap data structure, the sort heap, is presented. This heap is a simplification of the heap of Elmasry [SODA 2009: 471-476] and shares with it a O(loglogn) amortized-time Decrease-Key, but with a straightforward implementation such that our lower bound holds. Thus a natural model is presented for a pointer-based heap such that the amortized runtime of a self-adjusting structure and amortized lower asymptotic bounds for Decrease-Key differ by but a O(logloglogn) factor.

AB - A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Ω(log log n/log log log n) amortized time on the Decrease-Key operation (given O(logn) amortized-time Extract-Min). Intuitively, this bound shows the key to having O(1)-time Decrease-Key is the ability to sort O(logn) items in O(logn) time; Fibonacci heaps [M. .L. Fredman and R. E. Tarjan. J. ACM 34(3):596-615 (1987)] do this through the use of bucket sort. Our lower bound also holds no matter how much data is augmented; this is in contrast to the lower bound of Fredman [J. ACM 46(4):473-501 (1999)] who showed a tradeoff between the number of augmented bits and the amortized cost of Decrease-Key. A new heap data structure, the sort heap, is presented. This heap is a simplification of the heap of Elmasry [SODA 2009: 471-476] and shares with it a O(loglogn) amortized-time Decrease-Key, but with a straightforward implementation such that our lower bound holds. Thus a natural model is presented for a pointer-based heap such that the amortized runtime of a self-adjusting structure and amortized lower asymptotic bounds for Decrease-Key differ by but a O(logloglogn) factor.

UR - http://www.scopus.com/inward/record.url?scp=84904174074&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904174074&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-43948-7_53

DO - 10.1007/978-3-662-43948-7_53

M3 - Conference contribution

AN - SCOPUS:84904174074

SN - 9783662439470

VL - 8572 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 637

EP - 649

BT - Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings

PB - Springer Verlag

ER -