The problem of computing
a Kemeny optimal permutation
for a given collection of \(k\) full lists, for even integers \(k \geq 4\),
is NP-hard.
Minimum Feedback Edge Set
Minimum Feedback Edge Set
on Directed Graphs
Minimum Feedback Edge Set
on Directed Graphs
Minimum Feedback Edge Set
on Directed Graphs
Minimum Feedback Edge Set
on Directed Graphs
Minimum Feedback Edge Set
on Directed Graphs
Minimum Feedback Edge Set
on Directed Graphs
Minimum Feedback Edge Set
on Directed Graphs
Minimum Feedback Edge Set
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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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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.)
KRA Hardness
By Neeldhara Misra
KRA Hardness
- 241