  The centrality of a vertex v in a network intuitively captures how important
v is for communication in the network. The task of improving the centrality of
a vertex has many applications, as a higher centrality often implies a larger
impact on the network or less transportation or administration cost. In this
work we study the parameterized complexity of the NP-complete problems
Closeness Improvement and Betweenness Improvement in which we ask to improve a
given vertex' closeness or betweenness centrality by a given amount through
adding a given number of edges to the network. Herein, the closeness of a
vertex v sums the multiplicative inverses of distances of other vertices to v
and the betweenness sums for each pair of vertices the fraction of shortest
paths going through v. Unfortunately, for the natural parameter "number of
edges to add" we obtain hardness results, even in rather restricted cases. On
the positive side, we also give an island of tractability for the parameter
measuring the vertex deletion distance to cluster graphs.

Discrete Mathematics;Computational Complexity