## Abstract

Suppose we are given n moving postmen described by their motion equations p_{i}(t) = S_{i} + v_{i}t, i = 1,...,n, where S_{i} ∈ ℝ^{2} is the position of the ith postman at time t = 0, and v_{i} ∈ ℝ^{2} is his velocity. The problem we address is how to preprocess the postmen data so as to be able to efficiently answer two types of nearest-neighbor queries. The first one asks "who is the nearest postman at time t_{q} to a dog located at point s_{q}. In the second type a query dog is located at point s_{q} at time t_{q}, its speed is v_{q} > |v_{i}| (for all i = 1,...,n), and we want to know which postman the dog can catch first. The first type of query is relatively simple to address, the second type at first seems much more complicated. We show that the problems are very closely related, with efficient solutions to the first type of query leading to efficient solutions to the second. We then present two solutions to these problems, with tradeoff between preprocessing time and query time. Both solutions use deterministic data structures.

Original language | English |
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Pages (from-to) | 315-327 |

Number of pages | 13 |

Journal | Computational Geometry: Theory and Applications |

Volume | 6 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jan 1996 |

## Keywords

- Dynamic computational geometry
- Parametric search
- Persistent data structures
- Post-office problem
- Voronoi diagram

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics