## Abstract

We present an efficient algorithm for the following problem: Given a collection T = {δ _{1},...,δ _{n}} of n triangles in the plane, such that there exists a subset S ⊂ T (unknown to us), of ξ ≫ n triangles, such that ∪ _{δ∈ S}δ = ∪ _{δ∈T}δ construct efficiently the union of the triangles in T. We show that this problem can be solved in subquadratic time. In our solution, we use the approximate Disjoint-Cover (DC) algorithm, presented as a heuristics in [9]. We present a detailed implementation of this method, which combines a variety of techniques related to range-searching in two dimensions. We provide a rigorous analysis of its performance in the above setting, showing that it does indeed run in subquadratic time (for a reasonable range of ξ).

Original language | English |
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Pages | 413-422 |

Number of pages | 10 |

State | Published - 2004 |

Externally published | Yes |

Event | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States Duration: 11 Jan 2004 → 13 Jan 2004 |

### Conference

Conference | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country/Territory | United States |

City | New Orleans, LA. |

Period | 11/01/04 → 13/01/04 |