# The Complexity of the Residual Node Connectedness Reliability Problem

@article{Sutner1991TheCO, title={The Complexity of the Residual Node Connectedness Reliability Problem}, author={Klaus Sutner and Appajosyula Satyanarayana and Charles L. Suffel}, journal={SIAM J. Comput.}, year={1991}, volume={20}, pages={149-155} }

This paper considers a probabilistic network in which the edges are perfectly reliable but the nodes fail with some known probabilities. The network is in an operational state if the surviving nodes induce a connected graph. The residual node connectedness reliability $R(G)$ of a network G is the probability that the graph induced by the surviving nodes is connected. This reliability measure is very different from the widely studied K-terminal network reliability measure. It is proven that the… Expand

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#### References

SHOWING 1-4 OF 4 REFERENCES

The Complexity of Reliability Computations in Planar and Acyclic Graphs

- Mathematics, Computer Science
- SIAM J. Comput.
- 1986

We show that the problem of computing source-sink reliability is NP-hard, in fact # P-complete, even for undirected and acyclic directed source-sink planar graphs having vertex degree at most three.… Expand

Planar Formulae and Their Uses

- Mathematics, Computer Science
- SIAM J. Comput.
- 1982

Using these results, it is able to provide simple and nearly uniform proofs of NP-completeness for planar node cover, planar Hamiltonian circuit and line, geometric connected dominating set, and of polynomial space completeness forPlanar generalized geography. Expand

The Combinatorics of Network Reliability

- Computer Science
- 1987

The reliability polynominal Edge-disjoint subgraphs Additive and multiplicative improvements Combining the bounds The k-cycle bound Computational results References Index. Expand

The Complexity of Enumeration and Reliability Problems

- Mathematics, Computer Science
- SIAM J. Comput.
- 1979

For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems. Expand