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Efficient Connectivity Testing of Hypercubic Networks with Faults

  • Tomáš Dvořák
  • Jiří Fink
  • Petr Gregor
  • Václav Koubek
  • Tomasz Radzik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

Given a connected graph G and a set F of faulty vertices of G, let G − F be the graph obtained from G by deletion of all vertices of F and edges incident with them. Is there an algorithm, whose running time may be bounded by a polynomial function of |F| and log|V(G)|, which decides whether G − F is still connected? Even though the answer to this question is negative in general, we describe an algorithm which resolves this problem for the n-dimensional hypercube in time O(|F|n3). Furthermore, we sketch a more general algorithm that is efficient for graph classes with good vertex expansion properties.

Keywords

Connected Graph Interconnection Network Graph Class Local Connectivity Isoperimetric Problem 
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 2011

Authors and Affiliations

  • Tomáš Dvořák
    • 1
  • Jiří Fink
    • 1
  • Petr Gregor
    • 1
  • Václav Koubek
    • 1
  • Tomasz Radzik
    • 2
  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Department of Computer ScienceKing’s College LondonUnited Kingdom

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