Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-27T12:25:56.488Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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