### Abstract

We present a priority queue that supports the operations: insert in worst-case constant time, and delete, delete-min, find-min and decrease-key on an element x in worst-case O(lg(min{w_{x}, q_{x}} + 2)) time, where w_{x} (respectively, q_{x}) is the number of elements that were accessed after (respectively, before) the last access of x and are still in the priority queue at the time when the corresponding operation is performed. Our priority queue then has both the working-set and the queueish properties; and, more strongly, it satisfies these properties in the worst-case sense. We also argue that these bounds are the best possible with respect to the considered measures. Moreover, we modify our priority queue to satisfy a new unifying property - the time-finger property - which encapsulates both the working-set and the queueish properties. In addition, we prove that the working-set bound is asymptotically equivalent to the unified bound (which is the minimum per operation among the static-finger, static-optimality, and working-set bounds). This latter result is of tremendous interest by itself as it had gone unnoticed since the introduction of such bounds by Sleater and Tarjan [10]. Together, these results indicate that our priority queue also satisfies the static-finger, the static-optimality and the unified bounds.

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

Title of host publication | Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers |

Pages | 209-222 |

Number of pages | 14 |

Volume | 7056 LNCS |

DOIs | |

State | Published - 2011 |

Event | 22nd International Workshop on Combinatorial Algorithms, IWOCA 2011 - Vancouver, BC, Canada Duration: Jul 20 2011 → Jul 22 2011 |

### Publication series

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

Volume | 7056 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 22nd International Workshop on Combinatorial Algorithms, IWOCA 2011 |
---|---|

Country | Canada |

City | Vancouver, BC |

Period | 7/20/11 → 7/22/11 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers*(Vol. 7056 LNCS, pp. 209-222). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7056 LNCS). https://doi.org/10.1007/978-3-642-25011-8_17

**A unifying property for distribution-sensitive priority queues.** / Elmasry, Amr; Farzan, Arash; Iacono, John.

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

*Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers.*vol. 7056 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7056 LNCS, pp. 209-222, 22nd International Workshop on Combinatorial Algorithms, IWOCA 2011, Vancouver, BC, Canada, 7/20/11. https://doi.org/10.1007/978-3-642-25011-8_17

}

TY - GEN

T1 - A unifying property for distribution-sensitive priority queues

AU - Elmasry, Amr

AU - Farzan, Arash

AU - Iacono, John

PY - 2011

Y1 - 2011

N2 - We present a priority queue that supports the operations: insert in worst-case constant time, and delete, delete-min, find-min and decrease-key on an element x in worst-case O(lg(min{wx, qx} + 2)) time, where wx (respectively, qx) is the number of elements that were accessed after (respectively, before) the last access of x and are still in the priority queue at the time when the corresponding operation is performed. Our priority queue then has both the working-set and the queueish properties; and, more strongly, it satisfies these properties in the worst-case sense. We also argue that these bounds are the best possible with respect to the considered measures. Moreover, we modify our priority queue to satisfy a new unifying property - the time-finger property - which encapsulates both the working-set and the queueish properties. In addition, we prove that the working-set bound is asymptotically equivalent to the unified bound (which is the minimum per operation among the static-finger, static-optimality, and working-set bounds). This latter result is of tremendous interest by itself as it had gone unnoticed since the introduction of such bounds by Sleater and Tarjan [10]. Together, these results indicate that our priority queue also satisfies the static-finger, the static-optimality and the unified bounds.

AB - We present a priority queue that supports the operations: insert in worst-case constant time, and delete, delete-min, find-min and decrease-key on an element x in worst-case O(lg(min{wx, qx} + 2)) time, where wx (respectively, qx) is the number of elements that were accessed after (respectively, before) the last access of x and are still in the priority queue at the time when the corresponding operation is performed. Our priority queue then has both the working-set and the queueish properties; and, more strongly, it satisfies these properties in the worst-case sense. We also argue that these bounds are the best possible with respect to the considered measures. Moreover, we modify our priority queue to satisfy a new unifying property - the time-finger property - which encapsulates both the working-set and the queueish properties. In addition, we prove that the working-set bound is asymptotically equivalent to the unified bound (which is the minimum per operation among the static-finger, static-optimality, and working-set bounds). This latter result is of tremendous interest by itself as it had gone unnoticed since the introduction of such bounds by Sleater and Tarjan [10]. Together, these results indicate that our priority queue also satisfies the static-finger, the static-optimality and the unified bounds.

UR - http://www.scopus.com/inward/record.url?scp=81855228593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=81855228593&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-25011-8_17

DO - 10.1007/978-3-642-25011-8_17

M3 - Conference contribution

SN - 9783642250101

VL - 7056 LNCS

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

SP - 209

EP - 222

BT - Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers

ER -