Algorithm to find points that are furthest apart — better than O(n^2)?

Question

In my program, I have a set of points. For purposes of rescaling, I am searching for the two nodes that are furthest apart, and then computing a factor by which to multiply

Answer 1

The distance from A to B is the same as the distance from B to A. You can easily modify the algorithm to eliminate half of the computations this way. It'll still be O(n^2) but will be twice as fast.

That is, instead of computing all off-diagonal elements of the distance matrix P x P:

P = {A, B, C, D, ...}

  + A + B + C + D + ...
A |   | * | * | * | ...
B | * |   | * | * | ...
C | * | * |   | * | ...
D | * | * | * |   | ...
  |   |   |   |   |

you can compute either the upper triangle:

  + A + B + C + D + ...
A |   | * | * | * | ...
B |   |   | * | * | ...
C |   |   |   | * | ...
D |   |   |   |   | ...
  |   |   |   |   |

or the lower triangle:

  + A + B + C + D + ...
A |   |   |   |   | ...
B | * |   |   |   | ...
C | * | * |   |   | ...
D | * | * | * |   | ...
  |   |   |   |   |