  Centrality measures, quantifying the importance of vertices or edges, play a
fundamental role in network analysis. To date, triggered by some positive
approximability results, a large body of work has been devoted to studying
centrality maximization, where the goal is to maximize the centrality score of
a target vertex by manipulating the structure of a given network. On the other
hand, due to the lack of such results, only very little attention has been paid
to centrality minimization, despite its practical usefulness.
  In this study, we introduce a novel optimization model for local centrality
minimization, where the manipulation is allowed only around the target vertex.
We prove the NP-hardness of our model and that the most intuitive greedy
algorithm has a quite limited performance in terms of approximation ratio. Then
we design two effective approximation algorithms: The first algorithm is a
highly-scalable algorithm that has an approximation ratio unachievable by the
greedy algorithm, while the second algorithm is a bicriteria approximation
algorithm that solves a continuous relaxation based on the Lov\'asz extension,
using a projected subgradient method. To the best of our knowledge, ours are
the first polynomial-time algorithms with provable approximation guarantees for
centrality minimization. Experiments using a variety of real-world networks
demonstrate the effectiveness of our proposed algorithms: Our first algorithm
is applicable to million-scale graphs and obtains much better solutions than
those of scalable baselines, while our second algorithm is rather strong
against adversarial instances.
