A catalog of steiner tree formulations

We present some existing and some new formulations for the Steiner tree and Steiner arborescence problems. We show the equivalence of many of these formulations. In particular, we establish the equivalence between the classical bidirected dicut relaxation and two vertex weighted undirected relaxations. The motivation behind this study is a characterization of the feasible region of the dicut relaxation in the natural space corresponding to the Steiner tree problem. 0 7993 by John Wiley & Sons, Inc.

[1]  D. Gale.  A theorem on flows in networks , 1957 .

[2]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

[3]  J. Rhys.  A Selection Problem of Shared Fixed Costs and Network Flows , 1970 .

[4]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[5]  D. R. Fulkerson,et al.  Blocking and anti-blocking pairs of polyhedra , 1971, Math. Program..

[6]  D. R. Fulkerson,et al.  Packing rooted directed cuts in a weighted directed graph , 1974, Math. Program..

[7]  Yash P. Aneja,et al.  An integer linear programming approach to the steiner problem in graphs , 1980, Networks.

[8]  John E. Beasley.  An algorithm for the steiner problem in graphs , 1984, Networks.

[9]  Richard T. Wong,et al.  A dual ascent approach for steiner tree problems on a directed graph , 1984, Math. Program..

[10]  Pawel Winter,et al.  Steiner problem in networks: A survey , 1987, Networks.

[11]  Arie Segev,et al.  The node-weighted steiner tree problem , 1987, Networks.

[12]  N. Maculan.  The Steiner Problem in Graphs , 1987 .

[13]  Mihalis Yannakakis,et al.  Expressing combinatorial optimization problems by linear programs , 1991, STOC '88.

[14]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[15]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[16]  S. Chopra.  On the spanning tree polyhedron , 1989 .

[17]  Thomas L. Magnanti,et al.  A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design , 1989, Oper. Res..

[18]  Weiguo Liu.  A lower bound for the steiner tree problem in directed graphs , 1990, Networks.

[19]  Ronald L. Rardin,et al.  Polyhedral Characterization of Discrete Dynamic Programming , 1990, Oper. Res..

[20]  M. Yannakakis.  Expressing combinatorial optimization problems by linear programs , 1991, Symposium on the Theory of Computing.

[21]  명영수.  Valid Inequalities and Facets for the Steiner Problem in a Directed Graph , 1991 .

[22]  Young-Soo Myung.  Valid Inequalities and Facets for the Steinger Problem in a Directed Graph , 1991 .

[23]  R. Kipp Martin,et al.  Using separation algorithms to generate mixed integer model reformulations , 1991, Oper. Res. Lett..

[24]  Michel X. Goemans,et al.  Survivable networks, linear programming relaxations and the parsimonious property , 1993, Math. Program..

[25]  Michel X. Goemans,et al.  Arborescence Polytopes for Series-parallel Graphs , 1994, Discret. Appl. Math..

[26]  M. R. Rao,et al.  The Steiner tree problem I: Formulations, compositions and extension of facets , 1994, Math. Program..

[27]  Michel X. Goemans,et al.  The Steiner tree polytope and related polyhedra , 1994, Math. Program..

[28]  M. R. Rao,et al.  The Steiner tree problem II: Properties and classes of facets , 1994, Math. Program..