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Volumn 121, Issue 2, 2010, Pages 249-268

Copositive programming motivated bounds on the stability and the chromatic numbers

Author keywords

(fractional) Chromatic number; Copositive programming; Lov sz theta number; Semidefinite programming

Indexed keywords

MATHEMATICAL PROGRAMMING;

EID: 79952955093     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-008-0233-x     Document Type: Article
Times cited : (37)

References (33)
  • 1
    • 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 (2001)
    • (2001) J. Global Optim. , vol.24 , pp. 163-185
    • Bomze, I.M.1    De Klerk, E.2
  • 4
    • 33644895968 scopus 로고    scopus 로고
    • On np-hardness of the clique partition -independence number gap recognition and related problems
    • Busygin, S., Pasechnik, D.V.: On NP-hardness of the clique partition -independence number gap recognition and related problems. Discrete Math. 306(4), 460-463 (2006)
    • (2006) Discrete Math. , vol.306 , Issue.4 , pp. 460-463
    • Busygin, S.1    Pasechnik, D.V.2
  • 6
    • 0036433723 scopus 로고    scopus 로고
    • Approximation of the stability number of a graph via copositive programming
    • de Klerk, E., Pasechnik, D.V.: Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12, 875-892 (2002)
    • (2002) SIAM J. Optim. , vol.12 , pp. 875-892
    • De Klerk, E.1    Pasechnik, D.V.2
  • 7
    • 33846667310 scopus 로고    scopus 로고
    • Reduction of symmetric semidefinite programs using the regular representation
    • de Klerk, E., Pasechnik, D.V., Schrijver, A.: Reduction of symmetric semidefinite programs using the regular representation. Math. Program. 109(2-3), 613-624 (2007)
    • (2007) Math. Program. , vol.109 , Issue.2-3 , pp. 613-624
    • De Klerk, E.1    Pasechnik, D.V.2    Schrijver, A.3
  • 10
    • 33846706231 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for graph coloring andmaximal clique problems
    • Dukanovic, I., Rendl, F.: Semidefinite programming relaxations for graph coloring andmaximal clique problems. Math. Program. B 109(2), 345-366 (2007)
    • (2007) Math. Program. , vol.B 109 , Issue.2 , pp. 345-366
    • 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
    • 24944588682 scopus 로고    scopus 로고
    • Semidefinite bounds for the stability number of a graph via sums of squares of polynomials
    • Gvozdenovíc, N., Laurent, M.: Semidefinite bounds for the stability number of a graph via sums of squares of polynomials. Lect. Notes Comput. Sci. 3509, 136-151 (2005)
    • (2005) Lect. Notes Comput. Sci. , vol.3509 , pp. 136-151
    • Gvozdenovíc, N.1    Laurent, M.2
  • 14
    • 58149088531 scopus 로고    scopus 로고
    • Computing semidefinite programming lower bounds for the (fractional) chromatic number via block-diagonalization
    • to appear
    • Gvozdenovíc, N., Laurent, M.: Computing semidefinite programming lower bounds for the (fractional) chromatic number via block-diagonalization. SIAM J. Optim. (2008, to appear)
    • (2008) SIAM J. Optim.
    • Gvozdenovíc, N.1    Laurent, M.2
  • 15
    • 58149103431 scopus 로고    scopus 로고
    • The operator for the chromatic number of a graph
    • to appear
    • Gvozdenovi'c, N., Laurent, M.: The operator for the chromatic number of a graph. SIAM J. Optim. (2008, to appear)
    • (2008) SIAM J. Optim.
    • Gvozdenovi'c, N.1    Laurent, M.2
  • 16
    • 0036811821 scopus 로고    scopus 로고
    • Coloring k-colorable graphs using relatively small palettes
    • Halperin, E., Nathaniel, R., Zwick, U.: Coloring k-colorable graphs using relatively small palettes. J. Algorithms 45, 72-90 (2002)
    • (2002) J. Algorithms , vol.45 , pp. 72-90
    • Halperin, E.1    Nathaniel, R.2    Zwick, U.3
  • 17
    • 0032028848 scopus 로고    scopus 로고
    • Approximate graph coloring by semidefinite programming
    • Karger, D., Motwani, R., Sudan, M.: Approximate graph coloring by semidefinite programming. J. Assoc. Comput. Machinery 45, 246-265 (1998)
    • (1998) J. Assoc. Comput. Machinery , vol.45 , pp. 246-265
    • Karger, D.1    Motwani, R.2    Sudan, M.3
  • 19
    • 39649093787 scopus 로고    scopus 로고
    • On explicit exact sdp relaxation for nonlinear 0-1 programs
    • In: Ardal, K., Gerards, A.M.H. (eds.
    • Lasserre, J.B.: On explicit exact SDP relaxation for nonlinear 0-1 programs. In: Ardal, K., Gerards, A.M.H. (eds.) Lecture Notes in Computer Science, vol. 2081, pp. 293-303 (2001)
    • (2001) Lecture Notes in Computer Science , vol.2081 , pp. 293-303
    • Lasserre, J.B.1
  • 20
    • 84897579142 scopus 로고    scopus 로고
    • Strengthened semidefinite bounds for codes
    • Laurent, M.: Strengthened semidefinite bounds for codes. Preprint, p. 17 (2005)
    • (2005) Preprint , pp. 17
    • Laurent, M.1
  • 21
    • 33745858905 scopus 로고    scopus 로고
    • Semidefinite programming and integer programming
    • In: Weismantel, R., Aardal, K., Nemhauser, G. (eds.) Elsevier B. V Amsterdam
    • Laurent, M., Rendl, F.: Semidefinite programming and integer programming. In: Weismantel, R., Aardal, K., Nemhauser, G. (eds.) Handbook on Discrete Optimization, pp. 393-514. Elsevier B. V., Amsterdam (2005)
    • (2005) Handbook on Discrete Optimization, pp. , 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. Inform. Theory 25, 1-7 (1979)
    • (1979) IEEE Trans. Inform. 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
  • 24
    • 0002603293 scopus 로고
    • Practical graph isomorphism
    • McKay, B.D.: Practical graph isomorphism. Congressus Numerantium 30, 45-87 (1981)
    • (1981) Congressus Numerantium , vol.30 , pp. 45-87
    • McKay, B.D.1
  • 25
    • 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
  • 27
    • 39449110450 scopus 로고    scopus 로고
    • Computing the stability number of a graph via linear and semidefinite programming
    • Peña, J., Vera, J., Zuluaga, L.F.: Computing the stability number of a graph via linear and semidefinite programming. SIAM J. Optim. 18, 87-105 (2007)
    • (2007) SIAM J. Optim. , vol.18 , pp. 87-105
    • Peña, J.1    Vera, J.2    Zuluaga, L.F.3
  • 30
    • 0018492534 scopus 로고
    • A comparison of the delsarte and lovász bounds
    • Schrijver, A.: A comparison of the Delsarte and Lovász bounds. IEEE Trans. Inform. Theory IT 25, 425-429 (1979)
    • (1979) IEEE Trans. Inform. Theory IT , vol.25 , pp. 425-429
    • Schrijver, A.1
  • 33
    • 0000920501 scopus 로고    scopus 로고
    • Semidefinite optimization
    • Todd, M.J.: Semidefinite optimization. Acta Numerica 10, 515-560 (2001)
    • (2001) Acta Numerica , vol.10 , pp. 515-560
    • Todd, M.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.