Network Discovery and Verification with Distance Queries

  • Thomas Erlebach
  • Alexander Hall
  • Michael Hoffmann
  • Matúš Mihaľák
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


The network discovery (verification) problem asks for a minimum subset Q ⊆ V of queries in an undirected graph G = (V,E) such that these queries discover all edges and non-edges of the graph. In the distance query model, a query at node q returns the distances from q to all other nodes in the graph. In the on-line network discovery problem, the graph is initially unknown, and the algorithm has to select queries one by one based only on the results of previous queries. We give a randomized on-line algorithm with competitive ratio \(O(\sqrt{n\log{n}})\) for graphs on n nodes. We also show lower bounds of \(\Omega(\sqrt{n})\) and Ω(logn) on the competitive ratio of deterministic and randomized on-line algorithms, respectively. In the off-line network verification problem, the graph is known in advance and the problem is to compute a minimum number of queries that verify all edges and non-edges. We show that the problem is \(\mathcal{NP}\)-hard and present an O(logn)-approximation algorithm.


Competitive Ratio Vertex Cover IEEE INFOCOM Query Model Independence Number 
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 2006

Authors and Affiliations

  • Thomas Erlebach
    • 1
  • Alexander Hall
    • 2
  • Michael Hoffmann
    • 1
  • Matúš Mihaľák
    • 1
  1. 1.Department of Computer ScienceUniversity of Leicester 
  2. 2.Institute for Theoretical Computer ScienceETH Zürich 

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