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An efficient approach to determining the reliability of an undirected k-terminal network based on 2-terminal reliability functions is presented. First, a feasible set of (k-1) terminal-pairs is chosen, and the 2-terminal reliability functions of the (k-1) terminal-pairs are generated based on the edge expansion diagram using an OBDD (ordered binary decision diagram). Then the k-terminal reliability function can be efficiently constructed by combining these (k-1) reliability expressions with the Boolean and operation. Because building 2-terminal reliability functions and reducing redundant computations by merging reliability functions can be done very efficiently, the proposed approaches are much faster than those which directly expand the entire network or directly factor the k-terminal networks. The effectiveness of this approach is demonstrated by performing experiments on several large benchmark networks. An example of appreciable improvement is that the evaluation of the reliability of a source-terminal 3×10 all-terminal network took only 2.4 seconds on a SPARC 20 workstation. This is much faster than previous factoring-algorithms.