### Abstract

We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any "well-behaved" bound on the running time of the given BSTs, for any online access sequence. (A BST has a well-behaved bound with f(n) overhead if it spends at most O(f(n)) time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is O(log log n) competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive O(log log n) factor, and performs each access in worst-case O(log n) time.

Original language | English (US) |
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Title of host publication | Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings |

Pages | 388-399 |

Number of pages | 12 |

Volume | 7965 LNCS |

Edition | PART 1 |

DOIs | |

State | Published - 2013 |

Event | 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013 - Riga, Latvia Duration: Jul 8 2013 → Jul 12 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 7965 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013 |
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Country | Latvia |

City | Riga |

Period | 7/8/13 → 7/12/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings*(PART 1 ed., Vol. 7965 LNCS, pp. 388-399). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7965 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-39206-1_33

**Combining binary search trees.** / Demaine, Erik D.; Iacono, John; Langerman, Stefan; Özkan, Özgür.

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

*Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings.*PART 1 edn, vol. 7965 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 7965 LNCS, pp. 388-399, 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013, Riga, Latvia, 7/8/13. https://doi.org/10.1007/978-3-642-39206-1_33

}

TY - GEN

T1 - Combining binary search trees

AU - Demaine, Erik D.

AU - Iacono, John

AU - Langerman, Stefan

AU - Özkan, Özgür

PY - 2013

Y1 - 2013

N2 - We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any "well-behaved" bound on the running time of the given BSTs, for any online access sequence. (A BST has a well-behaved bound with f(n) overhead if it spends at most O(f(n)) time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is O(log log n) competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive O(log log n) factor, and performs each access in worst-case O(log n) time.

AB - We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any "well-behaved" bound on the running time of the given BSTs, for any online access sequence. (A BST has a well-behaved bound with f(n) overhead if it spends at most O(f(n)) time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is O(log log n) competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive O(log log n) factor, and performs each access in worst-case O(log n) time.

UR - http://www.scopus.com/inward/record.url?scp=84880317052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880317052&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-39206-1_33

DO - 10.1007/978-3-642-39206-1_33

M3 - Conference contribution

AN - SCOPUS:84880317052

SN - 9783642392054

VL - 7965 LNCS

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

SP - 388

EP - 399

BT - Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings

ER -