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1
d
If two rankings \(\sigma\) and \(\tau\)
are complete opposites,
then any ranking \(\rho\) will have
a total Kemeny distance of \({n \choose 2}\)
from both of them combined.
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This creates a neat
cancelation effect
& forces a minimum Kemeny score of
\(2{n \choose 2} + 2{m \choose 2} + 2m\)
on any ranking.
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d
This creates a neat
cancelation effect
& forces a minimum Kemeny score of
\(2{n \choose 2} + 2{m \choose 2} + 2m\)
on any ranking.
This creates a neat
cancelation effect
& forces a minimum Kemeny score of
\(2{n \choose 2} + 2{m \choose 2} + 2m\)
on any ranking.
+ 2k
if and only if G has a FES of size at most k.
final score \(\leq\)
(The cost of the backedges can be isolated.)