The Effect of Faults on Network Expansion

  title={The Effect of Faults on Network Expansion},
  author={Amitabha Bagchi and Ankur Bhargava and Amitabh Chaudhary and David Eppstein and Christian Scheideler},
  journal={Theory of Computing Systems},
We study the problem of how resilient networks are to node faults. Specifically, we investigate the question of how many faults a network can sustain and still contain a large (i.e., linear-sized) connected component with approximately the same expansion as the original fault-free network. We use a pruning technique that culls away those parts of the faulty network that have poor expansion. The faults may occur at random or be caused by an adversary. Our techniques apply in either case. In the… 

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  • 1994
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