  A network for the transportation of supplies can be described as a rooted
tree with a weight of a degree of congestion for each edge. We take the sum of
root-leaf distance (SRD) on a rooted tree as the whole degree of congestion of
the tree. Hence, we consider the SRD interdiction problem on trees with
cardinality constraint by upgrading edges (denoted by (SDIPTC) in brief). It
aims to maximize the SRD by upgrading the weights of $N$ critical edges such
that the total upgrade cost under some measurement is upper-bounded by a given
value. The relevant minimum cost problem (MCSDIPTC) aims to minimize the total
upgrade cost on the premise that the SRD is lower-bounded by a given value. We
develop two different norms including weighted $l_\infty$ norm and weighted
bottleneck Hamming distance to measure the upgrade cost. We propose two binary
search algorithms within O($n\log n$) time for the problems (SDIPTC) under the
two norms, respectively. For problems (MCSDIPTC),we propose two binary search
algorithms within O($N n^2$) and O($n \log n$) under weighted $l_\infty$ norm
and weighted bottleneck Hamming distance, respectively. These problems are
solved through their subproblems (SDIPT) and (MCSDIPT), in which we ignore the
cardinality constraint on the number of upgraded edges. Finally, we design
numerical experiments to show the effectiveness of these algorithms.
