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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
Richard M Karp; Rajeev Motwani; Prabhakar Raghavan |

OCLC Number: | 16902032 |

Description: | 30 pages : illustrations ; 28 cm. |

Series Title: | University of California, Berkeley.; Computer Science Division.; Report |

Responsibility: | Richard M. Karp, Rajeev Motwani, Prabhakar Raghavan. |

### Abstract:

We consider the problem of answering a series of on- line queries on a static data set. The conventional approach to such problems involves a preprocessing phase which constructs a data structure with good search behavior. The data structure representing the data set then remains fixed throughout the processing of the queries. Our approach involves dynamic or query driven structuring of the data set; our algorithm processes the data set only when doing so is required for answering a query. A data structure constructed progressively in this fashion is called a deferred data structure.

We develop the notion of deferred data structures by solving the problem of answering membership queries on an ordered set. We obtain a randomized algorithm which achieves asymptotically optimal performance with high probability. We then present optimal deferred data structures for the following problems in the plane: testing convex hull membership, half-plane intersection queries and fixed- constraint multi-objective linear programming. We also apply the deferred data structuring technique to multidimensional dominance query problems.

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