Geodesic
Inclusion-exclusion and network reliability
The electronic journal of combinatorics, Tome 5 (1998)
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Based on a recent improvement of the inclusion-exclusion principle, we present a new approach to network reliability problems. In particular, we give a new proof of a result of Shier, which expresses the reliability of a network as an alternating sum over chains in a semilattice, and a new proof of a result of Provan and Ball, which provides an algorithm for computing network reliability in pseudopolynomial time. Moreover, some results on $k$-out-of-$n$ systems are established.
DOI : 10.37236/1374
Classification : 60C05, 68M15, 90B18, 90B25
Mots-clés : \(k\)-out-of-\(n\) systems, inclusion-exclusion principle, network reliability 
@article{10_37236_1374,
     author = {Klaus Dohmen},
     title = {Inclusion-exclusion and network reliability},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1374},
     zbl = {0912.60020},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1374/}
}
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Klaus Dohmen. Inclusion-exclusion and network reliability. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1374

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