Balance Pools Into Bracket

[cblaze22]

I am trying to figure out an algorithm to balance a group of pools that go in a bracket.  The pools first have to be in a seeded order, but balanced at the same time, meaning teams in the same pool are on opposite sides if possible and seeds dont play the same seed if possible.

    A1, B1, C1, D1, A2, B2, C2, D2

Id like to match these games to this [link][1] found in the bracket.  I just can't figure out the best algorithm to find these games with a group of pools shown above which are 4 pools of 2.  I will need this done for bracket sizes of 16, 32, and 64 respectively.  Byes should also be taken into consideration, as if D2 dropped out and we only had 7 teams.

    Game 1: A1 vs C2
    Game 2: D1 vs B2
    Game 3: B1 vs D2
    Game 4: C1 vs A2

  [1]: http://www.printyourbrackets.com/8seeded.html

[wbport]

That is the same setup as used in swiss system tournaments.  Assuming eight seeded players, in rank the pairings will be 1-5, 6-2, 3-7, and 8-4.  This assumes some advantage to the first named player/team like white pieces or first serve and a coin toss could reverse all pairings.

In chess, the lowest rated (ranked/seeded) player would get a bye in case of a dropout or there are an odd number of competitors.  Assuming seven players (or eight with a dropout and the rest renumbered) and six and seven were unrated (unranked/unseeded), then five would get the bye.  Pairings would be 1-4, 6-2, 3-7, and 5 with a bye.

HTH

[cblaze22]

I dont know if I agree with that.  Here is a post of a larger problem.

http://stackoverflow.com/questions/17793675/balance-pools-into-a-bracket-algorithm

As you can see I want the quadrants of the bracket to not contain more then 1 team from a pool.  So all pools A1-A4 would be in different quadrants.