Output-Sensitive Construction of the Union of Triangles

Eti Ezra, Micha Sharir

Research output: Contribution to conferencePaperpeer-review

5 Scopus citations


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∈ Sδ = ∪ δ∈Tδ 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 languageEnglish
Number of pages10
StatePublished - 2004
Externally publishedYes
EventProceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States
Duration: 11 Jan 200413 Jan 2004


ConferenceProceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityNew Orleans, LA.


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