Generating facets for the independence system

SIAM Journal on Discrete Mathematics

Volumn 23, Issue 3, 2009, Pages 1484-1506

  Fouilhoux, Pierre ^a   Labbé, Martine ^b   Mahjoub, A Ridha ^c   Yaman, Handle ^d  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c UNIVERSITÉ PARIS DAUPHINE   (France)

^d BILKENT UNIVERSITY   (Turkey)

Author keywords

Independence system polytope; Integer programming; Lifting; Nonrank facets; Polyhedral combinatorics

Indexed keywords

COMBINATORIAL OPTIMIZATION;

FACET-DEFINING INEQUALITIES; INDEPENDENCE SYSTEM; INDUCED SUBGRAPHS; LIFTING; NONRANK FACETS; POLYHEDRAL COMBINATORICS; POLYTOPES; VALID INEQUALITY;

INTEGER PROGRAMMING;

EID: 73249118644     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/070695988     Document Type: Article

References (38)

1. E. BALAS, Facets of the knapsack polytope, Math. Programming, 8 (1975), pp. 146-164.
2. E. BALAS AND S. M. NG, On the set covering polytope: I. All the facets with coefficients in {0, 1, 2}, Math. Programming, 43 (1989), pp. 57-69.
3. E. BALAS AND S. M. NG, On the set covering polytope:II. Lifting the facets with coefficients in {0, 1, 2}, Math. Programming, 45 (1989), pp. 1-20.
4. E. BALAS AND E. ZEMEL, Facets of the knapsack polytope from minimal covers, SIAM J. Appl. Math., 34 (1978), pp. 119-148.
5. E. BALAS AND E. ZEMEL, Critical cutsets of graphs and ca nonical facets of set-packing polyhe-dra, Math. Oper. Res., 2 (1977), pp. 15-19.
6. F. BARAHONA, M. GRÖTSCHEL, AND A. R. MAHJOUB, Facets of the bipartite subgraph polytope, Math. Oper. Res., 10 (1985), pp. 340-358.
7. F. BARAHONA AND A. R. MAHJOUB, Facets of the balanced (acyclic) induced subgraph polytope, Math. Programming, 45 (1989), pp. 21-33.
8. F. BARAHONA AND A. R. MAHJOUB, Composition of graphs and polyhedra I: Balanced induced subgraphs and acyclic subgraphs, SIAM J. Discrete Math., 7 (1994), pp. 344-358.
9. F. BARAHONA AND A. R. MAHJ UB, Composition of graphs and polyhedra II: Stable sets,SIAM J. Discrete Math., 7 (1994), pp. 359-371.
10. F. BENDALI, A. R. MAHJOUB, AND J. MAILFERT. Composition of graphs and the triangle-free subgraph polytope, J. Combin. Optim., 6 (2002), pp. 351-389.
11. L. CÁNOVAS, M. LANDETE, AND A. MARÍN, New facets for the set packing polytope,Oper. Res. Lett., 27 (2000), pp. 153-161.
12. L. CÁNOVAS, M. LANDETE, AND A. MARAÍN, Facet obtaining procedures for set packing problems, SIAM J. Discrete Math., 16 (2003), pp. 127-155.
13. E. CHENG ANDW. H. CUNNINGHAM, Wheel inequalities for stable set polytopes, Math. Programming, 77 (1997), pp. 398-421.
14. E. cheng and s. DE vries, Antiweb-wheel inequalities and their separation problems over the stable set polytopes, Math. Program., 92 (2002), pp. 153-175.
15. V. CHVÁTAL, On certain polytopes associated with graphs, J. Combinatorial Theory Ser. B, 18 (1975), pp. 138-154.
16. i-covers I: Complexity and polytopes, Discrete Math., 58 (1986), pp. 121-142.
17. M. CONFORTI AND M. LAURENT, On the facial structure of independence system polyhedra, Math. Oper. Res., 13 (1988), pp. 543-555.
18. T. EASTON, K. HOOKER, AND E. K. LEE, Facets of the independent set polytope, Math. Program., 98 (2003), pp. 177-199.
19. R. EULER, M. JÚNGER, AND G. REINELT, Generalizations of cliques, odd cycles and anticycles and their relation to independence system polyhedra, Math. Oper. Res., 12 (1987), pp. 451-462.
20. R. EULER AND A. R. MAHJOUB, On a composition of independence systems by circuit identification, J. Combin. Theory Ser. B, 53 (1991), pp. 235-259.
21. P. FOUILHOUX AND A. R. MAHJOUB, Polyhedral results for the bipartite induced subgraph problem, Discrete Appl. Math., 154 (2006), pp. 2128-2149.
22. R. E. GOMORY, Some polyhedra related to combinatorial problems, Linear Algebra Appl., 2 (1969), pp. 451-558.
23. Z. GU, G. L. NEMHAUSER, AND M. W. P. SAVELSBERGH, Lifted cover inequalities for 0-1 integer programs: Computation, INFORMS J. Comput., 10 (1998), pp. 427-437.
24. P. L. HAMMER, E. L. JOHNSON, AND U. N. PELED, Facets of regular 0-1 polytopes, Math. Programming, 8 (1975), pp. 179-206.
25. M. LAURENT, A generalization of antiwebs to independence systems and their canonical facets, Math. Programming, 45 (1989), pp. 97-108.
26. R. MÜLLER AND A. S. SCHULZ, Transitive packing: A unifying concept in combinatorial optimization, SIAM J. Optim., 13 (2002), pp. 335-367.
27. G. L. NEMHAUSER AND L. E. TROTTER, Properties of vertex packing and independence system polyhedra, Math. Programming, 6 (1974), pp. 48-61.
28. G. L. NEMHAUSER AND L. A. WOLSEY, Integer and Combinatorial Optimization, John Wiley and Sons, New York, 1988.
29. P. NOBILI AND A. SASSANO, Facets and lifting procedures for the set covering polytope, Math. Programming, 43 (1989), pp. 111-137.
30. M. W. PADBERG, On the facial structure of set packing polyhedra, Math. Programming, 5 (1973), pp. 199-215.
31. M. W. PADBERG, On the complexity of set packing polyhedra, in Studies in Integer Programming, Ann. Discrete Math. 1, North-Holland, Amsterdam, 1977, pp. 421-434.
32. A. SASSANO, On the facial structure of the set covering polytope, Math. Programming, 44 (1989), pp. 181-202.
33. Y. SEKIGUCHI, A note on node packing polytopes on hypergraphs, Oper. Res. Lett., 2 (1983), pp. 243-247.
34. L. E. TROTTER, A class of facet producing graphs for vertex packing polyhedra, Discrete Math., 12 (1975), pp. 373-388.
35. R. WEISMANTEL, On the 0/1 knapsack polytope, Math. Programming, 77 (1997), pp. 49-68.
36. L. A. WOLSEY, Faces for a linear inequality in 0-1 variables, Math. Programming, 8 (1975), pp. 165-178.
37. L. A. WOLSEY, Facets and strong valid inequalities for integer programs, Oper. Res., 24 (1976), pp. 367-372.
38. L. A. WOLSEY, Further facet generating procedures for vertex packing polytopes, Math. Programming, 11 (1976), pp. 158-163.