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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)

Abstract

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).

Keywords

Maximum Degree Doubling Dimension Bound Degree Cross Edge Doubling Metrics 
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 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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