### Abstract

Recently, Har-Peled [17] presented a new randomized technique for online construction of the zone of a curve in a planar arrangement of arcs. In this paper: we present several applications of this technique, which yield improved solutions to a variety of problems. These applications include: (i) an efficient mechanism for performing online point location queries in an arrangement of arcs; (ii) an efficient algorithm for computing an approximation to the minimum-weight Steiner-tree of a set of points, where the weight is the number of intersections between the tree edges and a given collection of arcs; (iii) a subquadratic algorithm for cutting a set of pseudo-parabolas into pseudo-segments; (iv) an algorithm for cutting a set of line segments ('rods') in 3-space so as to eliminate all cycles in the vertical depth order; and (v) a near-optimal algorithm for reporting all bichromatic intersections between a set R of red arcs and a set B of blue arcs, where the unions of the arcs in each set are both connected.

Original language | English (US) |
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Title of host publication | Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 57-66 |

Number of pages | 10 |

State | Published - Dec 1 2001 |

Event | 2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: Apr 30 2001 → May 1 2001 |

### Publication series

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

Other | 2001 Operating Section Proceedings, American Gas Association |
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Country | United States |

City | Dallas, TX |

Period | 4/30/01 → 5/1/01 |

### Keywords

- Algorithms
- Design
- Theory
- Verification

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 57-66). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).