In this paper, a heuristic is proposed to find out the reliability of a directed network by using directed acyclic graph. This directed network has imperfect nodes as well as imperfect links. Directed acyclic graph based reliability computation involves three main steps: In the first step, built the reliability function of the given directed network which is the union of all min-paths from source to sink. In the second step, apply a heuristic approach to order the given communication links and nodes of the given directed network. Finally apply Shannon’s decomposition method to compute the reliability of the given directed network. The paper also shows that the reliability obtained by this method is equal to the reliability obtained by applying the classical inclusion-exclusion method on the given directed network.

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In this paper i have adopted an efficient approach for calculating the reliability of the computer communication network with the help of binary decision diagram. The computer communication network has imperfect nodes and imperfect links. It means the nodes as well as the communication links may fail with known probability. The network is represented in the form of a directed graph. First i have found the reliability of the given network by applying the inclusionexclusion formula, which is an exact method to find the reliability of a network and then i have found the reliability of the given network with binary decision diagram. To find the reliability via binary decision diagram, we must order the nodes and the communication links of the given network by applying a proposed heuristic approach. I have found that the reliability obtained via binary decision diagram is equal to the reliability obtained by inclusion-exclusion formula. I have also shown that the generated binary decision diagram is of the minimum size.

Binary Decision Diagrams and Its Variable Ordering for Disjoint Network Manoj Singhal Associate professor, Department of Information Technology, Accurate Institute of Management & Technology, Greater Noida (U.P.), India, Email: manoj_singhal@rediffmail.com Girish Sharma Associate Professor, Department of Computer Applications, Bhai Parmanand Institute of Business Studies, New Delhi Email: gkps123@gmail.com R. K. Chauhan Professor, Département of Computer Science and Applications, Kurukshetra University, Kurukshetra Email : rkchauhankuk@gmail.com

In this paper, I have considered a computer communication network which has perfect vertices and imperfect links. It means communication links may fail with known probability. I have found the reliability of the given network by using an exact method (inclusion-exclusion formula) and with binary decision diagram. I have found that the reliability obtained by both the method is same. Binary decision diagram based reliability evaluation involves three main steps. First ordering the given communication link by applying a heuristic approach. I have proposed a heuristic approach to generate the minimum size binary decision diagram. Second generate the reliability function with the help of min-paths from source to sink. At last apply Shannon's decomposition to compute the reliability of the given network.

Manoj Singhal, R. K. Chauhan, Girish Sharma, Asso. Prof., Dept. Of MCA, Academy of Business and Engineering Sciences, Ghaziabad, (U.P.), India, Email: manoj_singhal@rediffmail.com ## Prof. & Chairman, Deptt. Of Computer Science and Applications, Kurukshetra University, Kurukshetra, India, Email: rkc.dcsa@gmail.com ### Asstt. Prof., Deptt. Of MCA, Bhai Parmanand Institute Of Business Studies, Delhi, India, Email: gkps123@gmail.com

In this paper we adopted an efficient approach for generating the binary decision diagram of a computer communication network represented in the form of a directed graph for calculating the reliability of the computer communication network. We have shown that this binary decision diagram is of the minimum size. We have also generated modified binary decision diagrams of the given graph when a particular edge of this graph is down and these modified binary decision diagrams are of minimum size. Conclusively, we can say that if all min-paths of a network are disjoint, then more than one optimal ordering may be possible for finding the reliability of a computer communication network.