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Mathematical Problems in Engineering
Volume 2016, Article ID 6908120, 13 pages
Research Article

Decision Diagram Based Symbolic Algorithm for Evaluating the Reliability of a Multistate Flow Network

Guangxi Key Laboratory of Trusted Software, School of Computer Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, China

Received 11 July 2016; Revised 6 November 2016; Accepted 16 November 2016

Academic Editor: J.-C. Cortés

Copyright © 2016 Rongsheng Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Evaluating the reliability of Multistate Flow Network (MFN) is an NP-hard problem. Ordered binary decision diagram (OBDD) or variants thereof, such as multivalued decision diagram (MDD), are compact and efficient data structures suitable for dealing with large-scale problems. Two symbolic algorithms for evaluating the reliability of MFN, MFN_OBDD and MFN_MDD, are proposed in this paper. In the algorithms, several operating functions are defined to prune the generated decision diagrams. Thereby the state space of capacity combinations is further compressed and the operational complexity of the decision diagrams is further reduced. Meanwhile, the related theoretical proofs and complexity analysis are carried out. Experimental results show the following: (1) compared to the existing decomposition algorithm, the proposed algorithms take less memory space and fewer loops. (2) The number of nodes and the number of variables of MDD generated in MFN_MDD algorithm are much smaller than those of OBDD built in the MFN_OBDD algorithm. (3) In two cases with the same number of arcs, the proposed algorithms are more suitable for calculating the reliability of sparse networks.