A simple universal generating function method to search for all minimal paths in networks

Abstract

Evaluating network reliability is an important topic in planning, designing, and control of systems, and the minimal-path (MP) set is one of the fundamental tools for evaluating network reliability. A straightforward and simple algorithm is presented here for finding all MPs before calculating the binarystate network reliability between the source node and the sink node (i.e., one-to-one reliability). It is based on the universal generating function method (UGFM) and a generalized composition operator. The computational complexity of the proposed algorithm is also analyzed. Finally, an example is given to illustrate how all MPs are generated using the proposed UGFM. © 2009 IEEE.