On Path Cover Problems in Digraphs and Applications to Program Testing

  • Authors:
  • S. C. Ntafos;S. L. Hakimi

  • Affiliations:
  • Department of Mathematical Sciences, University of Texas at Dallas;-

  • Venue:
  • IEEE Transactions on Software Engineering
  • Year:
  • 1979

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Abstract

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.