Valid Inequalities and Facets for the Steiner Problem in a Directed Graph

  • Published : 1996.04.01

Abstract

In this paper, we describe the facial structure of the steiner problem in a directed graph by formulating it as set covering problem. We first characterize trivial facets and derive a necessary condition for nontrival facets. We also introduce a class of valid inequalities with 0-1 coefficients and show when such inequalities define facets.

Keywords

References

  1. Networks v.10 An integer linear programming approach to the steiner probelm in graphs Y.P.Aneja
  2. Mathematical Programming v.43 On the set covering polytope: Ⅰ. all the facets with coefficients in {0,1,2} E.Balas;S.M.NG
  3. Mathematics of Operations Research v.8 On the uncapacitated plant location problem Ⅰ: Valid inequalities and facets D.C. Cho;E.L.Jonson;M.W.Padberg;M.R.Rao
  4. Mathematics of Operations Research v.8 On the uncapacitated plant location problem Ⅰ: Facets and Lifting theorems D.C.Cho;M.W.Padberg;M.R.Rao
  5. Mathematical Programming v.64 The steiner tree problemⅠ: formulations, compositions and extension fo facets S.Chopra;M.R.Rao
  6. Mathematical Programming v.64 The steiner tree problem Ⅱ: properties and classes of facets S.Chopra;M.R.Rao
  7. Mathematical Programming v.23 Facets of the location polytope G.Cornuejols;J.M.Thizy
  8. Mathematical Programming v.43 On the 0.1 facets of the set covering polytope G.Cornuejols;A.Sassano
  9. Mathematical Programming v.6 Packing rooted directed cuts in a weighted directed graph D.R.Fulkerson
  10. Networks v.23 A catalog of steiner tree formulations M.X.Goemans;Y.s.Myung
  11. Annals of Discrete Mathematics v.31 Steiner problem in graphs N.Maculan
  12. Mathematical Programming v.44 On the facial structure of the set covering polytope A.Sassano
  13. Networks v.17 Steiner problem in networks: a survey P.Winter
  14. Mathematical Programming v.28 A dual ascent approach to steiner tree problems on a directed graph R.T.Wong