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The Parameterized Complexity of Centrality Improvement in Networks

  • Clemens Hoffmann
  • Hendrik Molter
  • Manuel Sorge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10706)

Abstract

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.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Clemens Hoffmann
    • 1
  • Hendrik Molter
    • 1
  • Manuel Sorge
    • 1
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.Department of Industrial Engineering and ManagementBen-Gurion University of the NegevBeer ShevaIsrael

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