Question

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Greatest linear dimension 2d set of points

I could compute the distance between each point and take the largest but that doesn’t sound like a very efficient way to do it when there are a large (> 1000) number of points.

Note: This is for iPhone so I don’t have a ton of processing power.

Answer 1

You’re asking to compute the diameter of the set. The standard technique is to first compute the convex hull, which reduces the problem to finding the diameter of a convex polygon. Even in the case where you don’t eliminate any points, this added information is exactly what’s needed to solve the problem efficiently. However, finding the diameter of a convex polygon is not entirely trivial; several published papers with algorithms for this task turn out to be incorrect.

Here’s a fairly readable discussion of a correct O(n) algorithm for the task (where n is the number of points in the convex hull).

Also, note the the iphone isn’t that limited; a carefully written implementation of even the completely naive algorithm can handle 1000 points in less than a tenth of a second. Of course, using the correct algorithm will let you go much faster =)