Issue No.05 - September (1979 vol.5)
S.C. Ntafos , Department of Mathematical Sciences, University of Texas at Dallas
In this paper various path cover problems, arising in program testing, are discussed. Dilworth's theorem for acyclic digraphs is generalized. Two methods for fmding a minimum set of paths (minimum path cover) that covers the vertices (or the edges) of a digraph are given. To model interactions among code segments, the notions of required pairs and required paths are introduced. It is shown that rmding a minimum path cover for a set of required pairs is NP-hard. An efficient algorithm is given for findng a minimum path cover for a set of required paths. Other constrained path problems are contsidered and their complexities are discussed.
required paths, Algorithmic complexity, Dilworth number, minimum path cover, must pairs, must paths, NP-hard, program testing, required pairs
S.C. Ntafos, S.L. Hakimi, "On Path Cover Problems in Digraphs and Applications to Program Testing", IEEE Transactions on Software Engineering, vol.5, no. 5, pp. 520-529, September 1979, doi:10.1109/TSE.1979.234213