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Volumn 109, Issue 2-3, 2007, Pages 345-365

Semidefinite programming relaxations for graph coloring and maximal clique problems

Author keywords

Chromatic number; Clique number; Cutting planes; Lov sz theta number

Indexed keywords

COMPUTATIONAL METHODS; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; NUMBER THEORY; POLYNOMIALS;

EID: 33846706231     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0026-z     Document Type: Conference Paper
Times cited : (55)

References (36)
  • 1
    • 0009062749 scopus 로고    scopus 로고
    • Approximating maximum stable set and minimum graph coloring problems with the positive semidefinite relaxation
    • Kluwer, Dordrecht
    • Benson, S., Ye, Y.: Approximating maximum stable set and minimum graph coloring problems with the positive semidefinite relaxation. In: Applications and Algorithms of Complementarity, pp. 1-18. Kluwer, Dordrecht (2000)
    • (2000) Applications and Algorithms of Complementarity , pp. 1-18
    • Benson, S.1    Ye, Y.2
  • 2
    • 0039772219 scopus 로고    scopus 로고
    • Solving large-scale sparse semidefinite programs for combinatorial optimization
    • Benson, S., Ye, Y., Zhang, X.: Solving large-scale sparse semidefinite programs for combinatorial optimization. SIAM J. Optim. 10, 443-461 (2000)
    • (2000) SIAM J. Optim , vol.10 , pp. 443-461
    • Benson, S.1    Ye, Y.2    Zhang, X.3
  • 3
    • 31244435061 scopus 로고    scopus 로고
    • Solving standard quadratic optimization problems via linear, semidefinite and copositive programming
    • Bomze, I.M., de Klerk, E.: Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. J. Global Optim. 24, 163-185 (2002)
    • (2002) J. Global Optim , vol.24 , pp. 163-185
    • Bomze, I.M.1    de Klerk, E.2
  • 4
    • 1542337156 scopus 로고    scopus 로고
    • A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
    • Burer, S., Monteiro, R.D.C.: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Program. 95, 329-357 (2003)
    • (2003) Math. Program , vol.95 , pp. 329-357
    • Burer, S.1    Monteiro, R.D.C.2
  • 5
    • 33747195800 scopus 로고    scopus 로고
    • Solving lift-and-project relaxations of binary integer programs
    • Burer, S., Vandenbussche, D.: Solving lift-and-project relaxations of binary integer programs. SIAM J. Optim. 16, 726-750 (2006)
    • (2006) SIAM J. Optim , vol.16 , pp. 726-750
    • Burer, S.1    Vandenbussche, D.2
  • 8
    • 33846670413 scopus 로고    scopus 로고
    • Semidefinite programming applied to graph coloring problem. PhD Thesis, University of Klagenfurt, Austria
    • forthcoming
    • Dukanovic, I.: Semidefinite programming applied to graph coloring problem. PhD Thesis, University of Klagenfurt, Austria (2006) (forthcoming)
    • Dukanovic, I.1
  • 9
    • 37049015975 scopus 로고    scopus 로고
    • A semidefinite programming based heuristic for graph coloring
    • to appear
    • Dukanovic, I., Rendl, F.: A semidefinite programming based heuristic for graph coloring. Discrete Appl. Math, (to appear)
    • Discrete Appl. Math
    • Dukanovic, I.1    Rendl, F.2
  • 10
    • 33846681828 scopus 로고    scopus 로고
    • Copositive programming motivated bounds on the clique and the chromatic number of a graph
    • Preprint
    • Dukanovic, I., Rendl, F.: Copositive programming motivated bounds on the clique and the chromatic number of a graph. Preprint (2006)
    • (2006)
    • Dukanovic, I.1    Rendl, F.2
  • 11
    • 2942659750 scopus 로고    scopus 로고
    • Symmetry groups, semidefinite programs, and sums of squares
    • Gatermann, K., Parrilo, P.A.: Symmetry groups, semidefinite programs, and sums of squares. J. Pure Appl. Algebra 192, 95-128 (2004)
    • (2004) J. Pure Appl. Algebra , vol.192 , pp. 95-128
    • Gatermann, K.1    Parrilo, P.A.2
  • 13
    • 0242511176 scopus 로고    scopus 로고
    • Computational experience with stable set relaxations
    • Gruber, G., Rendl, F.: Computational experience with stable set relaxations. SIAM J. Optim. 13,1014-1028 (2003)
    • (2003) SIAM J. Optim , vol.13 , pp. 1014-1028
    • Gruber, G.1    Rendl, F.2
  • 15
    • 0034415006 scopus 로고    scopus 로고
    • A spectral bundle method for semidefinite programming
    • Helmberg, G., Rendl, F.: A spectral bundle method for semidefinite programming. SIAM J. Optim. 10, 673-696 (2000)
    • (2000) SIAM J. Optim , vol.10 , pp. 673-696
    • Helmberg, G.1    Rendl, F.2
  • 16
    • 0023596413 scopus 로고
    • Using tabu search for graph coloring
    • Hertz, A., Werra, D.D.: Using tabu search for graph coloring. Computing 39, 345-351 (1987)
    • (1987) Computing , vol.39 , pp. 345-351
    • Hertz, A.1    Werra, D.D.2
  • 17
    • 0032028848 scopus 로고    scopus 로고
    • Approximate graph coloring by semidefinite programming
    • Mach, 1998
    • Karger, D., Motwani, R., Sudan, M.: Approximate graph coloring by semidefinite programming. J. Assoc. Comput. Mach. 45, 246-265 (1998)
    • J. Assoc. Comput , vol.45 , pp. 246-265
    • Karger, D.1    Motwani, R.2    Sudan, M.3
  • 18
    • 33846650853 scopus 로고    scopus 로고
    • Reduction of symmetric semidefinite programs using the regular *-representation
    • to appear
    • de Klerk, E., Pasechnik, D.V., Schrijver, A.: Reduction of symmetric semidefinite programs using the regular *-representation. Math. Program. (2005)(to appear)
    • (2005) Math. Program
    • de Klerk, E.1    Pasechnik, D.V.2    Schrijver, A.3
  • 19
    • 4344652238 scopus 로고    scopus 로고
    • On approximate graph colouring and max-k-cut algorithms based on the θ-function
    • de Klerk, E., Pasechnik, D.V., Warners, IE: On approximate graph colouring and max-k-cut algorithms based on the θ-function. J. Combinat. Optim. 8, 267-294 (2004)
    • (2004) J. Combinat. Optim , vol.8 , pp. 267-294
    • de Klerk, E.1    Pasechnik, D.V.2    Warners, I.E.3
  • 20
    • 33846709680 scopus 로고    scopus 로고
    • Knuth, D.E.: The sandwich theorem. Elect. J. Combinat. 1, 1-48 (1994)
    • Knuth, D.E.: The sandwich theorem. Elect. J. Combinat. 1, 1-48 (1994)
  • 21
    • 33745858905 scopus 로고    scopus 로고
    • Semidefmite programming and integer programming
    • R.W.e. K. Aardal G. Nemhauser ed, Elsevier, Amsterdam
    • Laurent, M., Rendl, F.: Semidefmite programming and integer programming. In: R.W.e. K. Aardal G. Nemhauser (ed.) Handbook on Discrete Optimization, pp. 393-514. Elsevier, Amsterdam (2005)
    • (2005) Handbook on Discrete Optimization , pp. 393-514
    • Laurent, M.1    Rendl, F.2
  • 22
    • 0018292109 scopus 로고
    • On the Shannon capacity of a graph
    • Lovász, L.: On the Shannon capacity of a graph. IEEE Trans. Inf. Theory 25, 1-7 (1979)
    • (1979) IEEE Trans. Inf. Theory , vol.25 , pp. 1-7
    • Lovász, L.1
  • 23
    • 0001154274 scopus 로고
    • Cones of matrices and set-functions and 0-1 optimization
    • Lovász, L., Schrijver, A.: Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. 1, 166-190 (1991)
    • (1991) SIAM J. Optim , vol.1 , pp. 166-190
    • Lovász, L.1    Schrijver, A.2
  • 25
    • 84947204236 scopus 로고    scopus 로고
    • Pruning by isomorphism in branch-and-cut
    • Margot, F.: Pruning by isomorphism in branch-and-cut. Lect. Notes Comput. Sci. 2081, 304-317 (2001)
    • (2001) Lect. Notes Comput. Sci , vol.2081 , pp. 304-317
    • Margot, F.1
  • 26
    • 33846677921 scopus 로고    scopus 로고
    • McEliece, J.R., Rodemich, E., Rumsey, H.: The Lovász bound and some generalizations. J. Combinat. Syst. Sci. 3, 134-1.52 (1978)
    • McEliece, J.R., Rodemich, E., Rumsey, H.: The Lovász bound and some generalizations. J. Combinat. Syst. Sci. 3, 134-1.52 (1978)
  • 27
    • 0002603293 scopus 로고
    • Practical graph isomorphism
    • McKay, B.D.: Practical graph isomorphism. Congressus Numer. 30, 45-87 (1981)
    • (1981) Congressus Numer , vol.30 , pp. 45-87
    • McKay, B.D.1
  • 28
    • 17444380875 scopus 로고    scopus 로고
    • Strengthening the Lovász θ(Ḡ) bound for graph coloring
    • Meurdesoif, P.: Strengthening the Lovász θ(Ḡ) bound for graph coloring. Math. Program. 102, 577-588 (2005)
    • (2005) Math. Program , vol.102 , pp. 577-588
    • Meurdesoif, P.1
  • 29
    • 0023452095 scopus 로고
    • Some NP-complete problems in quadratic and nonlinear programming
    • Murty, K.G., Kabadi, S.N.: Some NP-complete problems in quadratic and nonlinear programming. Math. Program. 39, 117-129 (1987)
    • (1987) Math. Program , vol.39 , pp. 117-129
    • Murty, K.G.1    Kabadi, S.N.2
  • 30
    • 33846699356 scopus 로고    scopus 로고
    • Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD Thesis, California Institute of Technology
    • Parrilo, P.A.: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD Thesis, California Institute of Technology (2000)
    • (2000)
    • Parrilo, P.A.1
  • 31
    • 33846665190 scopus 로고    scopus 로고
    • Parrilo, P.A., Sturmfels, B.: Minimizing polynomial functions. In: S. Basu, L.G.V. (eds.) Algorithmic and quantitative real algebraic geometry. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 60, pp. 83-99. AMS New york (2003)
    • Parrilo, P.A., Sturmfels, B.: Minimizing polynomial functions. In: S. Basu, L.G.V. (eds.) Algorithmic and quantitative real algebraic geometry. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 60, pp. 83-99. AMS New york (2003)
  • 32
    • 0018492534 scopus 로고
    • A comparison of the Delsarte and Lovász bounds
    • Schrijver, A.: A comparison of the Delsarte and Lovász bounds. IEEE Trans. Info. Theory IT-25, 425-429 (1979)
    • (1979) IEEE Trans. Info. Theory , vol.IT-25 , pp. 425-429
    • Schrijver, A.1
  • 33
    • 23844454333 scopus 로고    scopus 로고
    • New code upper bounds from the Terwilliger algebra
    • Schrijver, A.: New code upper bounds from the Terwilliger algebra. IEEE Trans. Infor. Theory 51, 2859-2866 (2004)
    • (2004) IEEE Trans. Infor. Theory , vol.51 , pp. 2859-2866
    • Schrijver, A.1
  • 35
    • 0036361611 scopus 로고    scopus 로고
    • Solving some large scale semidefinite programs via the conjugate residual method
    • Toh, K., Kojima, M.: Solving some large scale semidefinite programs via the conjugate residual method. SIAM J. Optim. 12, 669-691 (2002)
    • (2002) SIAM J. Optim , vol.12 , pp. 669-691
    • Toh, K.1    Kojima, M.2
  • 36
    • 0037117174 scopus 로고    scopus 로고
    • Improved lower bound on the Shannon capacity of C7
    • Vesel, A., Žerovnik, J.: Improved lower bound on the Shannon capacity of C7. Inf. Process. Lett. 81 (5), 277-282 (2002)
    • (2002) Inf. Process. Lett , vol.81 , Issue.5 , pp. 277-282
    • Vesel, A.1    Žerovnik, J.2


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