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Consecutive-2 systems on trees

Published online by Cambridge University Press:  27 July 2009

Miklos Santha  and
Yanjun Znang
Miklos Santha
Affiliation:
Laboratoire de Recherche InformatiqueUniversité Paris-Sud, 1405 Orsay. France
Yanjun Znang
Affiliation:
Computer Science DivisionUniversity of California Berkeley, California 94720
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Abstract

This paper studies consecutive-2 systems on trees. We show that given a set of probability values, the optimal assignment for binary trees depends on the particular values, whereas for k−regular trees, which are closely related to binary trees, it depends only on their relative ordering. In our proof, we introduce the notion of first-term-invariance, which might have further applications. We also show that the problem of computing the failure probability of consecutive-2 system is #P-complete in general, though the problem on trees is shown to be strongly polynomial.

Information

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 4 , October 1987 , pp. 441 - 456
Copyright
Copyright © Cambridge University Press 1987

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References

Chiang, D. & Niu, S.C. (1981). Reliability of consecutive k−out−of−n. IEEE Trans. Reliability R−30:87–89.CrossRefGoogle Scholar
Derman, C., Lieberman, G.J., & Ross, S.M. (1981). On the consecutive−k−out−n: F system. IEEE Trans. Reliability R−31 (1):57–63.Google Scholar
Du, D.Z. & Hwang, F.K. (1986). Optimal consecutive−2−out−of−n system. Math. Oper. Res. 11(1): 187–191.CrossRefGoogle Scholar
Du, D.Z. & Hwang, F.K. (1985). Optimal consecutive-2 systems of lines and cycles. Networks 15:439–447.CrossRefGoogle Scholar
Du, D.Z. & Hwang, F.K. (1987). Optimal assignments for consecutive-2 graphs. SIAM Alg. and Disc. Meth. 8:510–518.CrossRefGoogle Scholar
Du, D.Z. & Hwang, F.K. (1987). Reliabilities of consecutive 2-graphs. Prob. in Eng. and Info. Sciences 1 (3):293–298.CrossRefGoogle Scholar
Karp, R.M. & Luby, M. (1985). Monte-Carlo algorithms for the planar multiterminal network reliability problem. J. of Complexity 1:45–64.CrossRefGoogle Scholar
Provan, J.S. & Ball, M.O. (1983). The complexity of counting cuts and of computing the probability that a graph is connected. SIAM J. Comput. 12(1):777–788.CrossRefGoogle Scholar
Valiant, L.G. (1979). The complexity of enumeration and reliability problems. SIAM J. Comput. 8(3):410–421.CrossRefGoogle Scholar