On the cycle polytope of a directed graph

Networks

Volumn 36, Issue 1, 2000, Pages 34-46

  Balas, Egon ^a   Oosten, Maarten ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b Pros Revenue Management Inc   (United States)

Author keywords

Cycle polytope; Directed graph; Facet lifting; Projection; Traveling salesman polytope

Indexed keywords

EID: 0034239434     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/1097-0037(200008)36:1<34::AID-NET4>3.0.CO;2-2     Document Type: Article

References (15)

1. [1] E. Balas, The asymmetric assignment problem and some new facets of the traveling salesman polytope, SIAM J Discr Math 2 (1989), 425-451.
2. [2] E. Balas, The prize collecting traveling salesman problem. Networks 19 (1989), 621-636.
3. [3] E. Balas, The prize collecting traveling salesman problem: II. Polyhedral results, Networks 25 (1995), 199-216.
4. [4] E. Balas, On the cycle polytope of a directed graph, MSRR #593, GSIA, Carnegie Mellon University, Oct. 1993.
5. [5] E. Balas and M. Fischetti, A lifting procedure for the asymmetric traveling salesman polytope and a large new class of facets, Math Oper Res 16 (1993), 42-56.
6. [6] E. Balas and M. Fischetti, "On the monotonization of polyhedra," Integer Programming and Combinatorial Optimzation, Proc IPCO3, G. Rinaldi and L. Wolsey (Editors), CIACO, Louvain-la-Neuve, 1993, pp. 23-39.
7. [7] E. Balas and M. Oosten, On the dimension of projected polyhedra, Discr Appl Math 87 (1998), 1-9.
8. [8] P. Bauer, The circuit polytope: Facets, Math Oper Res 22 (1997), 110-145.
9. [9] C. Coullard and W.R. Pulleyblank, On cycle cones and polyhedra, Linear Alg Appl 114/115 (1989), 613-640.
10. [10] M. Fischetti, Facets of the asymmetric traveling salesman polytope, Math Oper Res 16 (1991), 42-56.
11. [11] M. Fischetti and P. Toth, "An additive approach for the optimal solution of the prize collecting traveling salesman problem," Vehicle routing: Methods and studies, B. Golden and A. Assad (Editors), North-Holland, New York, 1988, pp. 319-343.
12. [12] M. Grötschel, Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme, Hain Maisenheim am Glan, 1977.
13. [13] M. Grötschel and M. Padberg, "Polyhedral theory," The traveling salesman problem: A guided tour to combinatorial optimization, E. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D. Shmoys (Ediors), Wiley, New York, 1985, pp. 251-305.
14. [14] M. Oosten, A note on sequential lifting procedures, Research memorandum M 94-08, University of Limburg, Nov. 1994.
15. [15] P. Seymour, "Sums of circuits," Graph theory and related topics, J.A. Bondy and U.S.R. Murty (Editors), Academic Press, New York, 1979, pp. 341-355.