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Combinatorial Network Abstraction by Trees and Distances

  • Stefan Eckhardt
  • Sven Kosub
  • Moritz G. Maaß
  • Hanjo Täubig
  • Sebastian Wernicke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)

Abstract

This work draws attention to combinatorial network abstraction problems which are specified by a class  \(\mathcal{P}\) of pattern graphs and a real-valued similarity measure  \(\varrho\) based on certain graph properties. For fixed  \(\mathcal{P}\) and  \(\varrho\), the optimization task on any graph G is to find a subgraph G′ which belongs to  \(\mathcal{P}\) and minimizes \(\varrho(G,G^{\prime})\). We consider this problem for the natural case of trees and distance-based similarity measures. In particular, we systematically study spanning trees of graphs that minimize distances, approximate distances, and approximate closeness-centrality with respect to some standard vector and matrix norms. The complexity analysis shows that all considered variants of the problem are NP-complete, except for the case of distance-minimization with respect to the L  ∞  norm. We further show that unless P = NP, there exist no polynomial-time constant-factor approximation algorithms for the distance-approximation problems if a subset of edges can be forced into the spanning tree.

Keywords

Span Tree Planar Graph Matrix Norm Pattern Graph Admissible Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Stefan Eckhardt
    • 1
  • Sven Kosub
    • 1
  • Moritz G. Maaß
    • 1
  • Hanjo Täubig
    • 1
  • Sebastian Wernicke
    • 2
  1. 1.Fakultät für InformatikTechnische Universität MünchenGarchingGermany
  2. 2.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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