### Abstract

Several existing cache-oblivious dynamic dictionaries achieve O(log _{B} N) (or slightly better O(log_{B} N/M)) memory transfers per operation, where N is the number of items stored, M is the memory size, and B is the block size, which matches the classic B-tree data structure. One recent structure achieves the same query bound and a sometimes-better amortized update bound of O (1/B^{θ(1/log log B)2)} log_{B} N + 1/B log^{2} N) memory transfers. This paper presents a new data structure, the xDict, implementing predecessor queries in O(1/ε log_{B} N/M) worst-case memory transfers and insertions and deletions in O (1/εB ^{1-ε} log_{B} N/M) amortized memory transfers, for any constant ε with 0 < ε < 1. For example, the xDict achieves subconstant amortized update cost when N = M B°^{(B1-ε)}, whereas the B-tree's Θ(logB N/M) is subconstant only when N = o(MB), and the previously obtained Θ (1/B^{Θ(1/(log log B)2)} logB N + 1/B log^{2} N) is subconstant only when N = o(2^{√B}). The xDict attains the optimal tradeoff between insertions and queries, even in the broader external-memory model, for the range where inserts cost between Ω(1/B lg^{1+ε} N) and O(1/lg^{3} N) memory transfers.

Original language | English (US) |
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Title of host publication | Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms |

Publisher | Association for Computing Machinery (ACM) |

Pages | 1448-1456 |

Number of pages | 9 |

ISBN (Print) | 9780898717013 |

DOIs | |

State | Published - 2010 |

Event | 21st Annual ACM-SIAM Symposium on Discrete Algorithms - Austin, TX, United States Duration: Jan 17 2010 → Jan 19 2010 |

### Publication series

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

Other | 21st Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | Austin, TX |

Period | 1/17/10 → 1/19/10 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 1448-1456). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery (ACM). https://doi.org/10.1137/1.9781611973075.117