### Abstract

We present a novel connection between binary search trees (BSTs) and points in the plane satisfying a simple property. Using this correspondence, we achieve the following results: 1. A surprisingly clean restatement in geometric terms of many results and conjectures relating to BSTs and dynamic optimality. 2. A new lower bound for searching in the BST model, which subsumes the previous two known bounds of Wilber [FOCS'86]. 3. The first proposal for dynamic optimality not based on splay trees. A natural greedy but offline algorithm was presented by Lucas [1988], and independently by Munro [2000], and was conjectured to be an (additive) approximation of the best binary search tree. We show that there exists an equal-cost online algorithm, transforming the conjecture of Lucas and Munro into the conjecture that the greedy algorithm is dynamically optimal.

Original language | English (US) |
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Title of host publication | Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 496-505 |

Number of pages | 10 |

State | Published - Sep 21 2009 |

Event | 20th Annual ACM-SIAM Symposium on Discrete Algorithms - New York, NY, United States Duration: Jan 4 2009 → Jan 6 2009 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 20th Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | New York, NY |

Period | 1/4/09 → 1/6/09 |

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### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 496-505). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).