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Quantum Algorithms for Computational Geometry Problems

2020
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Theory of Quantum Computation, Communication, and Cryptography
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We study quantum algorithms for problems in computational geometry, such as Point-On-3-Lines problem. In this problem, we are given a set of lines and we are asked to find a point that lies on at least 3 of these lines. Point-On-3-Lines and many other computational geometry problems are known to be 3Sum-Hard. That is, solving them classically requires time Ω(n^{2-o(1)}), unless there is faster algorithm for the well known 3Sum problem (in which we are given a set S of n integers and have to

doi:10.4230/lipics.tqc.2020.9
dblp:conf/tqc/AmbainisL20
fatcat:uw54q4berbddbn7eaxeuutgwxq