Subject: 2-stage Group-KO System

Initial Parameters
------------------

n = # registered players
R = max # rounds in group qualification stage
S = max # rounds in KO finals

Even Groups
-----------

g = even group size
r = played group rounds

R odd  => g := R+1, r := R
R even => g := R,   r := R-1

Number of Groups Z and Handling of Rest Players Y
-------------------------------------------------

Z := round_up(n/g)

If Z <> n/g, then a group of
Y := n mod g 
rest players must be handled.
This rest group is filled up to g - 1 players.
For this take 1 player each out of 
g - 1 - (n mod g) 
randomly chosen other groups.
Then g - (n mod g) groups have one Bye each.

Player-Group-Distribution
-------------------------

Use either the mix strategy or the homogenous strategy.
Mix: Let sink the highest ranked player into one group 
at a time.
Homogenous: Fill a single group with the highest ranked
players left.

Round by round within each even group fix player 1 and 
let all others move one place clockwise. In an even group
with a Bye fix it instead.

KO Rounds s
-----------

s := min { S, round_down(ld(n/2)) }

The second parameter is an emergency measure ensuring
that the maximal power of 2 less than half of n is taken.

KO Participants k
-----------------

k := 2^s

They will have to win their way through a binary tree.

Seeding
-------

Pi; i=1..n is the place due to the placement conditions
(like points-direct_comparison-SODOS) after round r of 
player i in his group. The same place within a group 
may be reached by more than one player. Places are
numbered due to the order 1,2,..,g.

Q := { Pi | i=1..n } is the qualification pool of all 
players' places.

// seeding procedure
// all players of the remaining top places are seeded
// ,however, for the last free of all k finals' places
// random selection is done among equal qualification
// place getters

c := 0;
for (j:=1; j<=g; j++)
{
 M := { q in Q | q = j };
 c += |M|;
 IF (c<=k) {seed M; IF (c=k) break;}
 ELSE {randomly_select_and_seed k-c+|M| of M; break;}
}