Open Access
2013 On the 2-MRS Problem in a Tree with Unreliable Edges
Wei Ding, Yu Zhou, Guangting Chen, Hongfa Wang, Guangming Wang
J. Appl. Math. 2013: 1-11 (2013). DOI: 10.1155/2013/743908


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.


Download Citation

Wei Ding. Yu Zhou. Guangting Chen. Hongfa Wang. Guangming Wang. "On the 2-MRS Problem in a Tree with Unreliable Edges." J. Appl. Math. 2013 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950852
MathSciNet: MR3127455
Digital Object Identifier: 10.1155/2013/743908

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
Back to Top