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Effective Algorithm for Optimal K-Terminal Reliability of Distributed SystemSYREL (Hariri and Raghavendra, 1987) is applied to compute the reliability.The proposed heuristic algorithm is to maximize K-terminal reliability of a DS.The detailed steps for KTR are described in Appendix 1.ILLUSTRATIVE EXAMPLESExample 1Figure 2 illustrates the topology of a DS with eight nodes and eleven links. Theproblem involves determining a subset, K-terminal, of the DS which includessome of the nodes v 1 , v 2 , …, v 8 whose reliability is maximal.Fig. 2. The DS with eight nodes and eleven links.v 2 v 3 v 4e2,3 e 3,4p 1,2 =0.89 p 1,7 =0.81e 4,5 p 1,8 =0.93 p 2,3 =0.85v 1 e 1,2 v 8 e 4,8 v 5 p 3,4 =0.91 p 4,5 =0.82ee 4,6 1,8p 4,6 =0.83 p 4,8 =0.96e 1,7 e 6,8 p 5,6 =0.87 p 6,7 =0.84e 5,6 p 6,8 =0.88e 6,7v 7 v 6In Step 1, each node’s weight is evaluated using Eq. (1). The weight of v 1 ,v 2 , …, and v 8 are 0.998537, 0.9835, 0.9865, 0.9998898, 0.9766, 0.9995756,0.9696 and 0.999664, respectively. Therefore, v 4 is the node with maximalweight and is served as starting node for obtaining an adequate K-terminal.Notably, G k is {v 4 }.In Step 2, because ε s, j does not exist, set Eε( Gk )to empty.In Step 3, each link’s weight is evaluated using Eq. (2).In Step 4, let V tmp = V = ∅ , w V ε( Gk )(G k) = w(v s ), w( E Gk) = 0.109