메뉴 건너뛰기




Volumn 29, Issue 1, 2004, Pages 80-91

Separation algorithms for classes of STSP inequalities arising from a new STSP relaxation

Author keywords

Inequalities; Lifting; Node lifting; Polyhedron; Polytope; Separation; Symmetric traveling salesman problem

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; GRAPH THEORY; INTEGER PROGRAMMING; LINEAR PROGRAMMING; LINEAR SYSTEMS; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING; VECTORS;

EID: 4043088371     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.1030.0058     Document Type: Article
Times cited : (8)

References (27)
  • 3
    • 0000639521 scopus 로고
    • Small traveling salesman polytopes
    • Boyd, S., W. Cunningham. 1991. Small traveling salesman polytopes. Math. Oper. Res. 16 259-271.
    • (1991) Math. Oper. Res. , vol.16 , pp. 259-271
    • Boyd, S.1    Cunningham, W.2
  • 6
    • 84891647481 scopus 로고    scopus 로고
    • Separating over classes of TSP inequalities defined by 0-node lifting in polynomial time
    • Vancouver, British Columbia
    • Carr, R. 1996. Separating over classes of TSP inequalities defined by 0-node lifting in polynomial time. IPCO Proc. IPCO Conference, Vancouver, British Columbia, 460-474.
    • (1996) IPCO Proc. IPCO Conference , pp. 460-474
    • Carr, R.1
  • 7
    • 0031142588 scopus 로고    scopus 로고
    • Separating clique trees and bipartition inequalities having a fixed number of handles and teeth in polynomial time
    • Carr, R. 1997. Separating clique trees and bipartition inequalities having a fixed number of handles and teeth in polynomial time. Math. Oper. Res. 22(2) 257-265.
    • (1997) Math. Oper. Res. , vol.22 , Issue.2 , pp. 257-265
    • Carr, R.1
  • 8
    • 0041686616 scopus 로고    scopus 로고
    • Some results on node lifting of TSP inequalities
    • Carr, R. 2000. Some results on node lifting of TSP inequalities. J. Combin. Optim. 4(4) 395-414.
    • (2000) J. Combin. Optim. , vol.4 , Issue.4 , pp. 395-414
    • Carr, R.1
  • 9
    • 0033891487 scopus 로고    scopus 로고
    • Towards a 4/3 approximation for the asymmetric traveling salesman problem
    • San Francisco, CA
    • Carr, R., S. Vempala. 2000. Towards a 4/3 approximation for the asymmetric traveling salesman problem. SODA Conference, San Francisco, CA, 116-125.
    • (2000) SODA Conference , pp. 116-125
    • Carr, R.1    Vempala, S.2
  • 10
    • 0022129352 scopus 로고
    • The traveling salesman problem on a graph and some related integer polyhedra
    • Cornuejols, G., J. Fonlupt, D. Naddef. 1985. The traveling salesman problem on a graph and some related integer polyhedra. Math. Programming 33 1-27.
    • (1985) Math. Programming , vol.33 , pp. 1-27
    • Cornuejols, G.1    Fonlupt, J.2    Naddef, D.3
  • 11
    • 0001214263 scopus 로고
    • Maximum matching and a polyhedron with 0-1 vertices
    • Edmonds, J. 1965. Maximum matching and a polyhedron with 0-1 vertices. J. Res. National Bureau Standards 69B 125-130.
    • (1965) J. Res. National Bureau Standards , vol.69 B , pp. 125-130
    • Edmonds, J.1
  • 12
    • 0033076322 scopus 로고    scopus 로고
    • Separating maximally violated comb inequalities in planar graphs
    • Fleischer, L., E. Tardos. 1999. Separating maximally violated comb inequalities in planar graphs. Math. Oper. Res. 24(1) 130-148.
    • (1999) Math. Oper. Res. , vol.24 , Issue.1 , pp. 130-148
    • Fleischer, L.1    Tardos, E.2
  • 13
    • 0000699964 scopus 로고
    • Worst-case comparison of valid inequalities for the TSP
    • Goemans, M. X. 1995. Worst-case comparison of valid inequalities for the TSP. Math. Programming 69 335-349.
    • (1995) Math. Programming , vol.69 , pp. 335-349
    • Goemans, M.X.1
  • 14
    • 0000748672 scopus 로고
    • Multi-terminal network flows
    • Gomory, R. E., T. C. Hu. 1961. Multi-terminal network flows. SIAM J. Appl. Math. 9 551-570.
    • (1961) SIAM J. Appl. Math. , vol.9 , pp. 551-570
    • Gomory, R.E.1    Hu, T.C.2
  • 15
    • 34250263680 scopus 로고
    • On the symmetric traveling salesman problem II: Lifting theorems and facets
    • Grötschel, M., M. W. Padberg. 1979. On the symmetric traveling salesman problem II: Lifting theorems and facets. Math. Programming 16 282-302.
    • (1979) Math. Programming , vol.16 , pp. 282-302
    • Grötschel, M.1    Padberg, M.W.2
  • 17
    • 0002737249 scopus 로고
    • Computational complexity
    • E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys, eds., John Wiley & Sons, Chichester, U.K
    • Johnson, D. S., C. H. Papadimitriou. 1985. Computational complexity. E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys, eds. The Traveling Salesman Problem. John Wiley & Sons, Chichester, U.K., 37-85.
    • (1985) The Traveling Salesman Problem , pp. 37-85
    • Johnson, D.S.1    Papadimitriou, C.H.2
  • 18
    • 77957083042 scopus 로고
    • The traveling salesman problem
    • M. O. Ball, T. L. Magnanti, C. L. Monma, G. L. Nemhauser, eds., Elsevier Science B.V., Amsterdam, The Netherlands
    • Jünger, M., G. Reinelt, G. Rinaldi. 1995. The traveling salesman problem. M. O. Ball, T. L. Magnanti, C. L. Monma, G. L. Nemhauser, eds. Network Models, Handbooks in OR & MS, Vol. 7. Elsevier Science B.V., Amsterdam, The Netherlands, 225-330.
    • (1995) Network Models, Handbooks in OR and MS , vol.7 , pp. 225-330
    • Jünger, M.1    Reinelt, G.2    Rinaldi, G.3
  • 19
    • 0034247390 scopus 로고    scopus 로고
    • Separating a superclass of comb inequalities in planar graphs
    • Letchford, A. 2000. Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res. 25(3) 443-454.
    • (2000) Math. Oper. Res. , vol.25 , Issue.3 , pp. 443-454
    • Letchford, A.1
  • 20
    • 84868666177 scopus 로고    scopus 로고
    • Polynomial-time separation of simple comb inequalities
    • 2002, Cambridge, MA
    • Letchford, A., A. Lodi. 2002. Polynomial-time separation of simple comb inequalities. IPCO Proc., 2002, Cambridge, MA, 93-108.
    • (2002) IPCO Proc. , pp. 93-108
    • Letchford, A.1    Lodi, A.2
  • 22
    • 0027911602 scopus 로고
    • The graphical relaxation: A new framework for the symmetric traveling salesman polytope
    • Naddef, D., G. Rinaldi. 1993. The graphical relaxation: A new framework for the symmetric traveling salesman polytope. Math. Programming 58 53-88.
    • (1993) Math. Programming , vol.58 , pp. 53-88
    • Naddef, D.1    Rinaldi, G.2
  • 24
    • 0020092747 scopus 로고
    • Odd minimum cut sets and b-matchings
    • Padberg, M. W., M. R. Rao. 1982. Odd minimum cut sets and b-matchings. Math. Oper. Res. 7 67-80.
    • (1982) Math. Oper. Res. , vol.7 , pp. 67-80
    • Padberg, M.W.1    Rao, M.R.2
  • 25
    • 0010690078 scopus 로고
    • A branch-and-cut approach to a traveling salesman problem with side constraints
    • Padberg, M. W., G. Rinaldi. 1989. A branch-and-cut approach to a traveling salesman problem with side constraints. Management Sci. 35(11) 1393-1412.
    • (1989) Management Sci. , vol.35 , Issue.11 , pp. 1393-1412
    • Padberg, M.W.1    Rinaldi, G.2
  • 26
    • 0025448140 scopus 로고
    • Facet identification for the symmetric traveling salesman polytope
    • Padberg, M. W., G. Rinaldi. 1990. Facet identification for the symmetric traveling salesman polytope, Math. Programming 47 219-257.
    • (1990) Math. Programming , vol.47 , pp. 219-257
    • Padberg, M.W.1    Rinaldi, G.2
  • 27
    • 0026390010 scopus 로고
    • Expressing combinatorial optimization problems by linear programs
    • Yannakakis, M. 1991. Expressing combinatorial optimization problems by linear programs. J. Comp. System Sci. 43 441-466.
    • (1991) J. Comp. System Sci. , vol.43 , pp. 441-466
    • Yannakakis, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.