### Abstract

Splay trees are a self adjusting form of search tree that supports access operations in &Ogr;(log n) amortized time. Splay trees also have several amazing distribution sensitive properties, the strongest two of which are the working set theorem and the dynamic finger theorem. However, these two theorems are shown to poorly bound the performance of splay trees on some simple access sequences. The unified conjecture is presented, which subsumes the working set theorem and dynamic finger theorem, and accurately bounds the performance of splay trees over some classes of sequences where the existing theorems' bounds are not tight. While the unified conjecture for splay trees is unproven, a new data structure, the unified structure, is presented where the unified conjecture does hold. This structure also has a worst case of &Ogr;(log n) per operation, in contrast to the &Ogr;(n) worst case runtime of splay trees. A second data structure, the working set structure, is introduced. The working set structure has the same performance attributed to splay trees through the working set theorem, except the runtime is worst case per operation rather than amortized.

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

Title of host publication | Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 516-522 |

Number of pages | 7 |

State | Published - 2001 |

Event | 2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: Apr 30 2001 → May 1 2001 |

### Other

Other | 2001 Operating Section Proceedings, American Gas Association |
---|---|

Country | United States |

City | Dallas, TX |

Period | 4/30/01 → 5/1/01 |

### Fingerprint

### Keywords

- Algorithms
- Performance
- Theory
- Verification

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 516-522)

**Alternatives to splay trees with O(log n) worst-case access times.** / Iacono, John.

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

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms.*pp. 516-522, 2001 Operating Section Proceedings, American Gas Association, Dallas, TX, United States, 4/30/01.

}

TY - GEN

T1 - Alternatives to splay trees with O(log n) worst-case access times

AU - Iacono, John

PY - 2001

Y1 - 2001

N2 - Splay trees are a self adjusting form of search tree that supports access operations in &Ogr;(log n) amortized time. Splay trees also have several amazing distribution sensitive properties, the strongest two of which are the working set theorem and the dynamic finger theorem. However, these two theorems are shown to poorly bound the performance of splay trees on some simple access sequences. The unified conjecture is presented, which subsumes the working set theorem and dynamic finger theorem, and accurately bounds the performance of splay trees over some classes of sequences where the existing theorems' bounds are not tight. While the unified conjecture for splay trees is unproven, a new data structure, the unified structure, is presented where the unified conjecture does hold. This structure also has a worst case of &Ogr;(log n) per operation, in contrast to the &Ogr;(n) worst case runtime of splay trees. A second data structure, the working set structure, is introduced. The working set structure has the same performance attributed to splay trees through the working set theorem, except the runtime is worst case per operation rather than amortized.

AB - Splay trees are a self adjusting form of search tree that supports access operations in &Ogr;(log n) amortized time. Splay trees also have several amazing distribution sensitive properties, the strongest two of which are the working set theorem and the dynamic finger theorem. However, these two theorems are shown to poorly bound the performance of splay trees on some simple access sequences. The unified conjecture is presented, which subsumes the working set theorem and dynamic finger theorem, and accurately bounds the performance of splay trees over some classes of sequences where the existing theorems' bounds are not tight. While the unified conjecture for splay trees is unproven, a new data structure, the unified structure, is presented where the unified conjecture does hold. This structure also has a worst case of &Ogr;(log n) per operation, in contrast to the &Ogr;(n) worst case runtime of splay trees. A second data structure, the working set structure, is introduced. The working set structure has the same performance attributed to splay trees through the working set theorem, except the runtime is worst case per operation rather than amortized.

KW - Algorithms

KW - Performance

KW - Theory

KW - Verification

UR - http://www.scopus.com/inward/record.url?scp=0037858270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037858270&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0898714907

SP - 516

EP - 522

BT - Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms

ER -