Sparse Fault-Tolerant Spanners for Doubling Metrics with Bounded Hop-Diameter or Degree

  • T. -H. Hubert Chan
  • Mingfei Li
  • Li Ning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


We study fault-tolerant spanners in doubling metrics. A subgraph H for a metric space X is called a k-vertex-fault-tolerant t-spanner ((k,t)-VFTS or simply k-VFTS), if for any subset S ⊆ X with |S| ≤ k, it holds that d H ∖ S (x, y) ≤ t ·d(x, y), for any pair of x, y ∈ X ∖ S.

For any doubling metric, we give a basic construction of k-VFTS with stretch arbitrarily close to 1 that has optimal O(kn) edges. In addition, we also consider bounded hop-diameter, which is studied in the context of fault-tolerance for the first time even for Euclidean spanners. We provide a construction of k-VFTS with bounded hop-diameter: for m ≥ 2n, we can reduce the hop-diameter of the above k-VFTS to O(α(m, n)) by adding O(km) edges, where α is a functional inverse of the Ackermann’s function.

Finally, we construct a fault-tolerant single-sink spanner with bounded maximum degree, and use it to reduce the maximum degree of our basic k-VFTS. As a result, we get a k-VFTS with O(k 2 n) edges and maximum degree O(k 2).


Maximum Degree Doubling Dimension Bound Degree Cross Edge Doubling Metrics 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • T. -H. Hubert Chan
    • 1
  • Mingfei Li
    • 1
  • Li Ning
    • 1
  1. 1.The University of Hong KongHong Kong

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