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On the 2-MRS Problem in a Tree with Unreliable Edges

Author

Listed:
  • Wei Ding
  • Yu Zhou
  • Guangting Chen
  • Hongfa Wang
  • Guangming Wang

Abstract

This paper extends the well-known most reliable source (1-MRS) problem in unreliable graphs to the 2-most reliable source (2-MRS) problem. Two kinds of reachable probability models of node pair in unreliable graphs are considered, that is, the superior probability and united probability. The 2-MRS problem aims to find a node pair in the graph from which the expected number of reachable nodes or the minimum reachability is maximized. It has many important applications in large-scale unreliable computer or communication networks. The #P-hardness of the 2-MRS problem in general graphs follows directly from that of the 1-MRS problem. This paper deals with four models of the 2-MRS problem in unreliable trees where every edge has an independent working probability and devises a cubic-time and quadratic-space dynamic programming algorithm, respectively, for each model.

Suggested Citation

  • Wei Ding & Yu Zhou & Guangting Chen & Hongfa Wang & Guangming Wang, 2013. "On the 2-MRS Problem in a Tree with Unreliable Edges," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
    • Handle: RePEc:hin:jnljam:743908
    DOI: 10.1155/2013/743908
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    Cited by:

    1. Wei Ding & Ke Qiu, 2018. "A quadratic time exact algorithm for continuous connected 2-facility location problem in trees," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1262-1298, November.

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