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Journal of Mathematical Modelling and Algorithms

, Volume 11, Issue 3, pp 249–268 | Cite as

The Maximum Degree & Diameter-Bounded Subgraph and its Applications

  • Anthony Dekker
  • Hebert Pérez-RosésEmail author
  • Guillermo Pineda-Villavicencio
  • Paul Watters
Article

Abstract

We introduce the problem of finding the largest subgraph of a given weighted undirected graph (host graph), subject to constraints on the maximum degree and the diameter. We discuss some applications in security, network design and parallel processing, and in connection with the latter we derive some bounds for the order of the largest subgraph in host graphs of practical interest: the mesh and the hypercube. We also present a heuristic strategy to solve the problem, and we prove an approximation ratio for the algorithm. Finally, we provide some experimental results with a variety of host networks, which show that the algorithm performs better in practice than the prediction provided by our theoretical approximation ratio.

Keywords

Network design Degree/diameter problem Botnets Mesh 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Anthony Dekker
    • 1
  • Hebert Pérez-Rosés
    • 2
    Email author
  • Guillermo Pineda-Villavicencio
    • 1
  • Paul Watters
    • 1
  1. 1.Center for Informatics and Applied OptimizationUniversity of BallaratBallaratAustralia
  2. 2.Department of Computer ScienceThe University of NewcastleNewcastleAustralia

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