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Most Reliable Source on an Unreliable Tree Network with Faulty Vertices

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High Performance Networking, Computing, and Communication Systems (ICHCC 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 163))

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Abstract

In an unreliable communication network, failures may occur to vertices and/or edges. A node which maximizes the expected number of vertices reachable from it is called a most reliable source (MRS) of the network. The problem of computing a most reliable source of the network is one of the important network reliable problems. Most of previous studies focused on the case where each edge has an independent operational probability while all vertices are immune to failures. In this paper, we study another case where all edges are immune to failures while each vertex has an independent transmitting probability and an independent receiving probability. For such a tree network, we present a quadratic time algorithm based on a stack for computing an MRS of this network.

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References

  1. Ball, M.O., Lin, F.L.: A reliability model applied to emergency service vehicle location. Oper. Res. 41(1), 18–36 (1993)

    Article  MATH  Google Scholar 

  2. Ball, M.O., Provan, J.S., Shier, D.R.: Reliability Covering Problems. Networks 21(3), 345–357 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bondy, J.A., Murty, U.S.R.: Graph Theory with Application. Macmillan, London (1976)

    Book  MATH  Google Scholar 

  4. Colbourn, C.J.: The Combinatorics of Network Reliability. Oxford University Press, New York (1987)

    Google Scholar 

  5. Colbourn, C.J., Xue, G.: A linear time algorithm for computing the most reliable source on a series-parallel graph with unreliable edges. Theor. Comput. Sci. 209, 331–345 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ding, W.: Computing the Most Reliable Source on Stochastic Ring Networks. In: Proc. of WRI World Congress on Software Engineering 2009, Xiamen, China, May 19-21, vol. 1, pp. 345–347 (2009)

    Google Scholar 

  7. Melachrinoudis, E., Helander, M.E.: A single facility location problem on a tree with unreliable edges. Networks 27(3), 219–237 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mirchandani, P.B., Odoni, A.R.: Locations of medians on stochastic networks. Transport. Sci. 13, 85–97 (1979)

    Article  MathSciNet  Google Scholar 

  9. Nel, L.D., Colbourn, C.J.: Locating a broadcast facility in an unreliable network. INFOR. 28, 363–379 (1990)

    MATH  Google Scholar 

  10. Shier, D.R.: Network Reliability and Algebraic Structure. Oxford University Press, New York (1991)

    MATH  Google Scholar 

  11. Xue, G.: Linear time algorithms for computing the most reliable source on an unreliable tree network. Networks 30(1), 37–45 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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© 2011 Springer-Verlag Berlin Heidelberg

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Ding, W. (2011). Most Reliable Source on an Unreliable Tree Network with Faulty Vertices. In: Wu, Y. (eds) High Performance Networking, Computing, and Communication Systems. ICHCC 2011. Communications in Computer and Information Science, vol 163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25002-6_25

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  • DOI: https://doi.org/10.1007/978-3-642-25002-6_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25001-9

  • Online ISBN: 978-3-642-25002-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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