Well, in a half an hour I have to go to some boring 3h meeting and have to have something to think about. If you want, you can think about it, too. And here goes the challenge:

Let's say we have 8 machines, each communicates with every other one. Amount of data, which is exchanged between every two machines is defined (

perl -le "for$x(0..7){for$y($x+1..7){$f[$x][$y]=$f[$y][$x]=int rand 10
+0}}
$f[$_][$_]='-' for 0..7; print join' ', @$_ for @f"

[download]
):

 - 38 72 79 58 88 59 33
38  - 70 71 27 47 77 14
72 70  - 90 42 63 56 90
79 71 90  - 60 57 21 95
58 27 42 60  - 28 33 52
88 47 63 57 28  - 11 85
59 77 56 21 33 11  - 59
33 14 90 95 52 85 59  -

Now, we have to find such division of these 8 machines into two groups of 4 machines, that exchange of data between these two groups is minimal.

Original problem was, as my friend gave it to me, for 64 machines, and then result: two 32-machines groups had to be divided further to 4 16-machines groups, etc.

Brute force algorithm (C++) had problems even with 8 machines, now, after 6 years it should be little better. But it's not about brute force, is it? As I remember, we did something heuristic, we didn't found optimal solution. But as I have 6 years more experience and a meeting will be long, and nothing better to do, let's find some solution :)

Update 2009-03-12 08:47 GMT: "Divide" challenge app added

In reply to "Divide" challenge by grizzley

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