In the Maximum Connectivity Improvement (MCI) problem, we are given a
directed graph G=(V,E) and an integer B and we are asked to find B new
edges to be added to G in order to maximize the number of connected pairs of
vertices in the resulting graph. The MCI problem has been studied from the
approximation point of view. In this paper, we approach it from the
parameterized complexity perspective in the case of directed acyclic graphs. We
show several hardness and algorithmic results with respect to different natural
parameters. Our main result is that the problem is W[2]-hard for parameter
B and it is FPT for parameters ∣V∣−B and ν, the matching number of
G. We further characterize the MCI problem with respect to other
complementary parameters.Comment: 15 pages, 1 figur