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Effective Algorithm for Optimal K-Terminal Reliability of Distributed SystemK-terminal and m represents the number of paths of a selected K-terminal (Haririand Raghavendra, 1987). In the proposed algorithm, in the worst case, thecomplexity of evaluating the weight of each node is O(e) and each link is O(e × n),selecting an adequate K-terminal is O(n 3 ), and computing the reliability of theK-terminal using SYREL is O(m 2 ) (Hariri and Raghavendra, 1987). Therefore, thecomplexity of the proposed algorithm is max(O(n 3 ), O(m 2 )).Table 2. Random Method for Three DS Topologies with Eight Nodes.T(s) Lr K request AES HitR ARErrR UpErrBnd UpErrBndR ARErrRlnk ARErrRT4 0.326084 0 0.763126 0.417357 0.9577363 0.503812 0 0.829212 0.733091 0.9648452 0.886631 20 0.644896 0.842723 0.949601 0.7457454 0.638387 0 0.327150 0.320436 0.4794673 0.732953 0 0.355200 0.381432 0.5550652 0.963593 10 0.339181 0.457403 0.568255 0.3405104 0.897291 0 0.062130 0.081107 0.0916023 0.951859 0 0.088845 0.128657 0.1402032 0.987630 0 0.065677 0.138905 0.141486 0.072217 0.3861574 0.667060 0 0.532687 0.607786 0.8072013 0.716601 0 0.713274 0.890054 0.9245012 0.936734 0 0.369311 0.692768 0.734436 0.538424Ring (n8e8)Bridge (n8e11)(Fig. 3.)0.0~1.00.5~1.00.8~1.00.0~1.04 0.937299 0 0.195759 0.316703 0.3921773 0.965475 0 0.149418 0.318579 0.3194032 0.984210 0 0.094193 0.208457 0.214969 0.1464574 0.991387 0 0.042027 0.065841 0.0658413 0.997596 0 0.027991 0.056993 0.0571172 0.998858 0 0.018207 0.047118 0.04732 0.029408 0.230964 0.558898 0 0.561959 0.483877 0.9513213 0.759641 10 0.338054 0.395725 0.7486392 0.952303 0 0.388869 0.029266 0.648013 0.4296274 0.956241 0 0.048489 0.094668 0.0965773 0.972747 10 0.048654 0.103147 0.1049872 0.996003 20 0.041780 0.148503 0.151313 0.0463084 0.997204 10 0.003449 0.008865 0.0089143 0.998569 0 0.004190 0.009181 0.0091932 0.999521 0 0.002618 0.005022 0.005032 0.003419 0.159785Average 2.9 0.261346 (0.295691) (0.412415) 0.261346 0.261346Hypercube (n8e12)0.5~1.00.8~1.00.0~1.00.5~1.00.8~1.0T(s): represents the topology (size) of a DS.Lr : the range of link’s reliability, the reliability is obtained by random generator.AES : the value of average exact solution whose value is[ Σ( DSR opt]/( total simulation cases ).HitR : the ratio of obtaining exact solution.ARErrR : the value of ( Σ[ 1 −( DSRapp / DSRopt )])/( total simulation cases ) .113