Abstract
An approach to finding a minimal set of base paths of a program is described. The program digraph is reduced to a weighted loopfree graph (WLFG) in which a node represents a subgraph of the program digraph that contains at most one outermost loop of the program. An algorithm for finding a maximal cutset of the WLFG is given such that (1) a maximal cutset does not contain two arcs that lie on a single path of the WLFG, and (2) its capacity is equal to the cardinality of a minimal set of base paths of the program. The algorithm repeatedly finds an eliminable arc and removes it from the WLFG until either the WLFG contains three nodes or no more eliminable arc can be found. An illustration is given for finding a maximal cutset and subsequently a minimal set of base paths.
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Koh, H., Chuang, H.Y.H. Finding a minimal set of base paths of a program. International Journal of Computer and Information Sciences 8, 473–488 (1979). https://doi.org/10.1007/BF00995499
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DOI: https://doi.org/10.1007/BF00995499