[lbsvduqo] double elimination tournament structure

the basic gadget of the middle rounds of a double elimination tournament can be described as follows.

there are N contestants still competing.  the gadget will reduce the number of contestants to N/2.

group A is the winners' bracket and has N/2 contestants.  group D is the losers' bracket and has N/2 contestants.

group A (N/2 contestants) pairs off and plays a round of games, which we call Miniround 1-Upper.  Miniround 1-Upper produces two groups.  the winners of Miniround 1-Upper form the new group A, containing N/4 contestants.  the losers form group B with N/4 contestants.

group D (N/2 contestants) pairs off and plays a round of games, which we call Miniround 1-Lower.  the losers of Miniround 1-Lower are eliminated.  the winners form group C with N/4 contestants.

Miniround 1-Upper and Miniround 1-Lower can happen in parallel.

after these rounds complete, remaining are new group A, group B, and group C, for a total of 3N/4 contestants.

next, group B and C combine (totaling N/2 contestants) and pair off, playing Miniround 2 in the losers's bracket.  the winners of Miniround 2 form the new group D with N/4 contestants.  the losers of Miniround 2 are eliminated.

in the end, we have new group A with N/4 contestants and new group D with N/4 contestants, for a total of N/2 contestants, ready to be fed through the gadget again.

the contestants in the losers' bracket play two games (Miniround 1-{Upper or Lower} then Miniround 2) during the time the winners of the winners' bracket play only one game (Miniround 1-Upper).  being in the losers' bracket is doubly tiring.  this fact is not obvious in small double-elimination tournaments, and is obscured by the fact that group D is initially empty so some of the initial losers' bracket rounds are skipped.

we have not specified exactly how pairing happens in Miniround 1-Upper, Miniround 1-Lower, and Miniround 2.  there are several desirable goals which probably cannot all be met simultaneously.

1. avoid for as long as possible contestants who have already met in the winners' bracket from meeting again in the losers' bracket.
2. the strongest contestants (perhaps defined by seeding) advance as far as possible.
3. define a fixed bracket before the tournament starts.

#2 could be satisfied by dynamic pairing (violating #3) before each round.  the highest seeds get paired against the lowest seeds.  however, some might call this unfair, and a structure not fixed in advance might be confusing.  also this may require more travel if there are multiple sites.

variation: the losers' bracket (group D) could start filled, perhaps with contestants from a second-tier league.  they start with one virtual loss on their records.

variation: omit Miniround 1-Lower.  group D and group B combine (totaling 3N/4 contestants) and are partitioned into triplets.  this can be done in games like poker which can have more than two contestants in a game.  the one victor from each triplet forms the new group D (N/4 contestants).  this round cannot be done in parallel with Miniround 1-Upper because group B has not been produced yet.  however, it could be done in parallel with Miniround 1-Upper of the next iteration of the gadget.  at the end, the winner of the winners' bracket will have to wait (get to rest) for the losers' bracket to complete.

if the initial number of contestants is not a power of 2, is it a simple matter of using the next largest power of 2 and assigning byes to the weakest seeds?

can this gadget be straightforwardly generalized to triple elimination and beyond?