# Subquadratic Algorithms for Some \textsc{3Sum}-Hard Geometric Problems in the Algebraic Decision Tree Model

@inproceedings{Aronov2021SubquadraticAF, title={Subquadratic Algorithms for Some \textsc\{3Sum\}-Hard Geometric Problems in the Algebraic Decision Tree Model}, author={Boris Aronov and Mark de Berg and Jean Cardinal and Esther Ezra and John Iacono and Micha Sharir}, year={2021} }

We present subquadratic algorithms in the algebraic decision-tree model for several 3Sumhard geometric problems, all of which can be reduced to the following question: Given two sets A, B, each consisting of n pairwise disjoint segments in the plane, and a set C of n triangles in the plane, we want to count, for each triangle ∆ ∈ C, the number of intersection points between the segments of A and those of B that lie in ∆. The problems considered in this paper have been studied by Chan (2020… Expand

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