Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 388/731
5. Nets and coalitions 3. Coalition Formation
Theorem 5.29 (CS
CS-Search-1 up to Layer l)
With the algorithm CS-Search-1 we get the
following bound for k after searching through
layer l:
{
⌈ |A|
h
⌉ if |A| ≡ h − 1 mod h and |A| ≡ l mod 2,
⌊ |A|
h ⌋ otherwise.
where h = def ⌊ |A|−l
2
⌋ + 2.
Thus, for l = |A| (check the top node), k
switches from |A| to |A|
2 .