### Abstract

It is shown that the online binary search tree data structure GreedyASS performs asymptotically as well on a sufficiently long sequence of searches as any static binary search tree where each search begins from the previous search (rather than the root). This bound is known to be equivalent to assigning each item i in the search tree a positive weight w_{i} and bounding the search cost of an item in the search sequence si,..., s_{m} (Equation presented) This result is the strongest finger-type bound to be proven for binary search trees. By setting the weights to be equal, one observes that our bound implies the dynamic finger bound. Compared to the previous proof of the dynamic finger bound for Splay trees, our result is significantly shorter, stronger, simpler, and has reasonable constants.

Original language | English (US) |
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Title of host publication | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |

Publisher | Association for Computing Machinery |

Pages | 672-691 |

Number of pages | 20 |

Volume | 1 |

ISBN (Print) | 9781510819672 |

State | Published - 2016 |

Event | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States Duration: Jan 10 2016 → Jan 12 2016 |

### Other

Other | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |
---|---|

Country | United States |

City | Arlington |

Period | 1/10/16 → 1/12/16 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016*(Vol. 1, pp. 672-691). Association for Computing Machinery.

**Weighted dynamic finger in binary search trees.** / Iacono, John; Langerman, Stefan.

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

*27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016.*vol. 1, Association for Computing Machinery, pp. 672-691, 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, United States, 1/10/16.

}

TY - GEN

T1 - Weighted dynamic finger in binary search trees

AU - Iacono, John

AU - Langerman, Stefan

PY - 2016

Y1 - 2016

N2 - It is shown that the online binary search tree data structure GreedyASS performs asymptotically as well on a sufficiently long sequence of searches as any static binary search tree where each search begins from the previous search (rather than the root). This bound is known to be equivalent to assigning each item i in the search tree a positive weight wi and bounding the search cost of an item in the search sequence si,..., sm (Equation presented) This result is the strongest finger-type bound to be proven for binary search trees. By setting the weights to be equal, one observes that our bound implies the dynamic finger bound. Compared to the previous proof of the dynamic finger bound for Splay trees, our result is significantly shorter, stronger, simpler, and has reasonable constants.

AB - It is shown that the online binary search tree data structure GreedyASS performs asymptotically as well on a sufficiently long sequence of searches as any static binary search tree where each search begins from the previous search (rather than the root). This bound is known to be equivalent to assigning each item i in the search tree a positive weight wi and bounding the search cost of an item in the search sequence si,..., sm (Equation presented) This result is the strongest finger-type bound to be proven for binary search trees. By setting the weights to be equal, one observes that our bound implies the dynamic finger bound. Compared to the previous proof of the dynamic finger bound for Splay trees, our result is significantly shorter, stronger, simpler, and has reasonable constants.

UR - http://www.scopus.com/inward/record.url?scp=84963522569&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963522569&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781510819672

VL - 1

SP - 672

EP - 691

BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

PB - Association for Computing Machinery

ER -