What is the best algorithm to find if any three points are collinear in a set of points say n. Please also explain the complexity if it is not trivial.
Thanks
Bala
What is the best algorithm to find if any three points are collinear in
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What is the best algorithm to find if any three points are collinear in a set of points say n. Please also explain the complexity if it is not trivial.
Thanks
Bala
If you can come up with a better than O(N^2) algorithm, you can publish it!
This problem is 3-SUM Hard, and whether there is a sub-quadratic algorithm (i.e. better than O(N^2)) for it is an open problem. Many common computational geometry problems (including yours) have been shown to be 3SUM hard and this class of problems is growing. Like NP-Hardness, the concept of 3SUM-Hardness has proven useful in proving ‘toughness’ of some problems.
For a proof that your problem is 3SUM hard, refer to the excellent surver paper here: http://www.cs.mcgill.ca/~jking/papers/3sumhard.pdf
Your problem appears on page 3 (conveniently called 3-POINTS-ON-LINE) in the above mentioned paper.
So, the currently best known algorithm is O(N^2) and you already have it 🙂