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 


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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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