### 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 - 2009 |

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

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

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

**The geometry of binary search trees.** / Demaine, Erik D.; Harmon, Dion; Iacono, John; Kane, Daniel; Pǎtraşcu, Mihai.

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

*Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms.*pp. 496-505, 20th Annual ACM-SIAM Symposium on Discrete Algorithms, New York, NY, United States, 1/4/09.

}

TY - GEN

T1 - The geometry of binary search trees

AU - Demaine, Erik D.

AU - Harmon, Dion

AU - Iacono, John

AU - Kane, Daniel

AU - Pǎtraşcu, Mihai

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70349130339&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349130339&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780898716801

SP - 496

EP - 505

BT - Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms

ER -