Abstract
Given a weighted matroid
M
and a positive integer
K
, the
K
th best base of
M
problem is to find
K
distinct minimum (or maximum) bases regarding the weight function. This problem is NP-hard. We prove that it is polynomial for 2-sums of uniform matroids and a fixed number of
k
-sums of series parallel graphs,
M
(
K
4
)
,
W
3
,
Q
6
and
P
6
.