I'd say that the problem is a bit underspecified. Two trivial solution spring into mind, both more or less fitting the specification. Obviously, neither extreme is what you want, but what do you want? Are there any limits on the number of clumps, the number of complaints per clumb, the maximum distance between any pair of complaints per clumb? Do you have an expressions in terms of complaints, clumbs, distances that you want to minimize?

Even if you say something like that you want sqrt(N) of clumps, there will be solutions that you probably do not wish - you could make a scanline parallel to the Y-axis and make a sweep. Each time your scanline hits a complaint, you increment a counter. If the counter hits k * sqrt(N), the last sqrt(N) encountered complaints are put together into a clump.

The hardest part is to come up with the specifictation: what do you want to minimize/maximize/minmax/maxmin? That will determine whether this problem is trivial to solve, or very hard. I've already shown trivial solutions, but it isn't hard to come up with specification that will quickly reduce problems like the travelling salesman, or 0-1 knapsack to an instance of the described problem.

Abigail

In reply to Re: Sorting by geographical proximity / clumping groups of items based on X and Y by Abigail-II
in thread Sorting by geographical proximity / clumping groups of items based on X and Y by vroom

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