Output-sensitive construction of the union of triangles

We present an efficient algorithm for the following problem: Given a collection T = {1, . . . , n} of n triangles in the plane, such that there exists a subset S T (unknown to us) of n triangles, such that S = T , construct efficiently the union of the triangles in T. We show that this problem can be solved in randomized expected time O(n4/3 log n + n log2 n), which is subquadratic for = o(n/ log2 n). In our solution, we use a variant of the method of Br

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Eti Ezra, Micha Sharir
• Keywords: Algorithms, Finite Vc-dimension, Randomized Expected Time, Set Cover, SODA 2004