Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
by Mathias 6. January 2012 07:08

I just came across this interesting homework problem on StackOverflow:

Given a group of n items, each with a distinct value V(i), what is the best way to divide the items into 3 groups so the group with the highest value is minimized? Give the value of this largest group.

This looks like one of these combinatorial problems where a deterministic algorithm exists, and will be guaranteed to identify the optimal solution, with the small caveat that larger problem may take an extremely long time to resolve.

Note that as ccoakley points out in his comment to the StackOverflow question, there is no reason for a greedy approach to produce the optimal answer.

I figured this would be a good test for Bumblebee, my Artificial Bee Colony algorithm, which can produce a good solution in reasonable time, at the cost of not being guaranteed to find the actual optimum solution.

While we are at it, I figured we could also relax the constraints, and break the group into an arbitrary number of groups, and have possible duplicates rather than unique values.



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