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Volumn 19, Issue 2, 2008, Pages 592-615

Computing semidefinite programming lower bounds for the (fractional) chromatic number via block-diagonalization

Author keywords

Chromatic number; Hamming graph; Kneser graph; Lov sz theta number; Semidefinite programming; Terwilliger algebra

Indexed keywords

CHROMATIC NUMBER; HAMMING GRAPH; KNESER GRAPH; SEMIDEFINITE PROGRAMMING; TERWILLIGER ALGEBRA;

EID: 58149088531     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/070683520     Document Type: Article
Times cited : (19)

References (38)
  • 2
    • 3543090051 scopus 로고    scopus 로고
    • Maximum stable set formulations and heuristics based on continuous optimization
    • S. BURER, R. MONTEIRO, AND Y. ZHANG, Maximum stable set formulations and heuristics based on continuous optimization, Math. Program. Ser. A, 94 (2002), pp. 137-166.
    • (2002) Math. Program. Ser. A , vol.94 , pp. 137-166
    • BURER, S.1    MONTEIRO, R.2    ZHANG, Y.3
  • 3
    • 9744253091 scopus 로고    scopus 로고
    • Bounding vertex coloring by truncated multistage branch and bound
    • M. CARAMIA AND P. DELL'OLMO, Bounding vertex coloring by truncated multistage branch and bound, Networks, 44 (2004), pp. 231-242.
    • (2004) Networks , vol.44 , pp. 231-242
    • CARAMIA, M.1    DELL'OLMO, P.2
  • 4
    • 37049034859 scopus 로고    scopus 로고
    • Coloring graphs by iterated local search traversing feasible and infeasible solutions
    • M. CARAMIA AND P. DELL'OLMO, Coloring graphs by iterated local search traversing feasible and infeasible solutions, Discrete Appl. Math., 156 (2008), pp. 201-217.
    • (2008) Discrete Appl. Math , vol.156 , pp. 201-217
    • CARAMIA, M.1    DELL'OLMO, P.2
  • 6
    • 0000971541 scopus 로고
    • Edmonds polytopes and a hierarchy of combinatorial problems
    • V. CHVÁTAL, Edmonds polytopes and a hierarchy of combinatorial problems, Discrete Math., 4 (1973, pp. 305-337.
    • (1973) Discrete Math , vol.4 , pp. 305-337
    • CHVÁTAL, V.1
  • 8
    • 37149037448 scopus 로고    scopus 로고
    • Efficient algorithms for finding critical subgraphs
    • C. DESROSIERS, P. GALINIER, AND A. HERTZ, Efficient algorithms for finding critical subgraphs, Discrete Appl. Math., 156 (2008), pp. 244-266.
    • (2008) Discrete Appl. Math , vol.156 , pp. 244-266
    • DESROSIERS, C.1    GALINIER, P.2    HERTZ, A.3
  • 9
    • 33846706231 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for graph coloring and maximal clique problems
    • I. DUKANOVIC AND F. RENDL, Semidefinite programming relaxations for graph coloring and maximal clique problems, Math. Program., 109 (2007), pp. 345-365.
    • (2007) Math. Program , vol.109 , pp. 345-365
    • DUKANOVIC, I.1    RENDL, F.2
  • 10
    • 37049015975 scopus 로고    scopus 로고
    • A semidefinite programming based heuristic for graph coloring
    • I. DUKANOVIC AND F. RENDL, A semidefinite programming based heuristic for graph coloring, Discrete Appl. Math., 156 (2008), pp. 180-189.
    • (2008) Discrete Appl. Math , vol.156 , pp. 180-189
    • DUKANOVIC, I.1    RENDL, F.2
  • 11
    • 67649459593 scopus 로고    scopus 로고
    • I. DUKANOVIC AND F. RENDL, Coposüiυe Programming Motivated Bounds on the Clique and the Chromatic Number, http://www.optimization-online.org/DB-HTML/2006/05/1403. html (2006).
    • I. DUKANOVIC AND F. RENDL, Coposüiυe Programming Motivated Bounds on the Clique and the Chromatic Number, http://www.optimization-online.org/DB-HTML/2006/05/1403. html (2006).
  • 12
    • 0000965650 scopus 로고    scopus 로고
    • Hybrid evolutionary algorithms for graph coloring
    • P. GALINIER AND J.-K. HAO, Hybrid evolutionary algorithms for graph coloring, J. Comb. Optim., 3 (1999), pp. 379-397.
    • (1999) J. Comb. Optim , vol.3 , pp. 379-397
    • GALINIER, P.1    HAO, J.-K.2
  • 13
    • 37049006713 scopus 로고    scopus 로고
    • An adaptive memory algorithm for the k-colouring problem
    • P. GALINIER, A. HERTZ, AND N. ZUFFEREY, An adaptive memory algorithm for the k-colouring problem, Discrete Appl. Math., 156 (2008), pp. 267-279.
    • (2008) Discrete Appl. Math , vol.156 , pp. 267-279
    • GALINIER, P.1    HERTZ, A.2    ZUFFEREY, N.3
  • 16
    • 67649489505 scopus 로고    scopus 로고
    • Approximating the Stability Number and the Chromatic Number of a Graph via Semidefinite Programming, Ph.D. thesis, University of Amsterdam
    • N. GVOZDENOVIC, Approximating the Stability Number and the Chromatic Number of a Graph via Semidefinite Programming, Ph.D. thesis, University of Amsterdam, 2008.
    • (2008)
    • GVOZDENOVIC, N.1
  • 17
    • 58149103431 scopus 로고    scopus 로고
    • The operator ψ for the chromatic number of a graph
    • N. GVOZDENOVIC AND M. LAURENT, The operator ψ for the chromatic number of a graph, SIAM J. Optim., 19 (2008), pp. 572-591
    • (2008) SIAM J. Optim , vol.19 , pp. 572-591
    • GVOZDENOVIC, N.1    LAURENT, M.2
  • 18
    • 0032028848 scopus 로고    scopus 로고
    • Approximate graph coloring by semidefinite programming
    • D. KARGER, R. MOTWANI, AND M. SUDAN, Approximate graph coloring by semidefinite programming, J. ACM, 45 (1998), pp. 246-265.
    • (1998) J. ACM , vol.45 , pp. 246-265
    • KARGER, D.1    MOTWANI, R.2    SUDAN, M.3
  • 19
    • 39649093787 scopus 로고    scopus 로고
    • An explicit exact SDP relaxation for nonlinear 0-1 programs
    • Integer Programming and Combinatorial Optimization, K. Aardal and A. M. H. Gerards, eds, Springer-Verlag, Berlin
    • J. B. LASSERRE, An explicit exact SDP relaxation for nonlinear 0-1 programs, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 2081, K. Aardal and A. M. H. Gerards, eds., Springer-Verlag, Berlin, 2001, pp. 293-303.
    • (2001) Lecture Notes in Comput. Sci , vol.2081 , pp. 293-303
    • LASSERRE, J.B.1
  • 20
    • 0141517272 scopus 로고    scopus 로고
    • A comparison of the Sherali-Adams, Loυάsz-Schrijver and Lasserre relaxations for 0 - 1 programming
    • M. LAURENT, A comparison of the Sherali-Adams, Loυάsz-Schrijver and Lasserre relaxations for 0 - 1 programming, Math. Oper. Res., 28 (2003), pp. 470-496.
    • (2003) Math. Oper. Res , vol.28 , pp. 470-496
    • LAURENT, M.1
  • 21
    • 33846653263 scopus 로고    scopus 로고
    • Strengthened semidefinite programming bounds for codes
    • M. LAURENT, Strengthened semidefinite programming bounds for codes, Math. Program., 109 (2007), pp. 239-261.
    • (2007) Math. Program , vol.109 , pp. 239-261
    • LAURENT, M.1
  • 22
    • 33745858905 scopus 로고    scopus 로고
    • Semidefinite programming and integer programming
    • K. Aardal, G. Nemhauser, and R. Weismantel, eds, Elsevier B.V, New York
    • M. LAURENT AND F. RENDL, Semidefinite programming and integer programming, in Handbook on Discrete Optimization, K. Aardal, G. Nemhauser, and R. Weismantel, eds., Elsevier B.V., New York, 2005, pp 393-514.
    • (2005) Handbook on Discrete Optimization , pp. 393-514
    • LAURENT, M.1    RENDL, F.2
  • 23
    • 34648860385 scopus 로고
    • Kneser's conjecture, chromatic numbers and homotopy
    • L. LOVÁSZ, Kneser's conjecture, chromatic numbers and homotopy, J. Combin. Theory Ser. A, 25 (1978), pp. 319-324.
    • (1978) J. Combin. Theory Ser. A , vol.25 , pp. 319-324
    • LOVÁSZ, L.1
  • 24
    • 0018292109 scopus 로고
    • On the Shannon capacity of a graph
    • L. LOVÁSZ, On the Shannon capacity of a graph. IEEE Trans. Inform. Theory, 25 (1979, pp. 1-7.
    • (1979) IEEE Trans. Inform. Theory , vol.25 , pp. 1-7
    • LOVÁSZ, L.1
  • 25
    • 9244246569 scopus 로고    scopus 로고
    • Topological lower bounds for the chromatic number: A hierarchy
    • J. MATOUSEK AND G. ZIEGLER, Topological lower bounds for the chromatic number: A hierarchy, Jahresber. Deutsch. Math.-Verein., 106 (2004), pp. 71-90.
    • (2004) Jahresber. Deutsch. Math.-Verein , vol.106 , pp. 71-90
    • MATOUSEK, J.1    ZIEGLER, G.2
  • 26
    • 33644602434 scopus 로고    scopus 로고
    • A branch-and-cut algorithm for graph coloring
    • I. M. MÉNDEZ-DIAZ AND P. ZABALA, A branch-and-cut algorithm for graph coloring, Discrete Appl. Math., 154 (2006), pp. 826-847.
    • (2006) Discrete Appl. Math , vol.154 , pp. 826-847
    • MÉNDEZ-DIAZ, I.M.1    ZABALA, P.2
  • 27
    • 37049026884 scopus 로고    scopus 로고
    • A cutting plane algorithm for graph coloring
    • I. MÉNDEZ-DIAZ AND P. ZABALA, A cutting plane algorithm for graph coloring, Discrete Appl. Math., 156 (2008), pp. 159-179.
    • (2008) Discrete Appl. Math , vol.156 , pp. 159-179
    • MÉNDEZ-DIAZ, I.1    ZABALA, P.2
  • 28
    • 17444380875 scopus 로고    scopus 로고
    • Strengthening the Loυász θ (G) bound for graph coloring
    • P. MEURDESOIF, Strengthening the Loυász θ (G) bound for graph coloring, Math. Program., 102 (2005), pp. 577-588.
    • (2005) Math. Program , vol.102 , pp. 577-588
    • MEURDESOIF, P.1
  • 29
    • 33751550994 scopus 로고    scopus 로고
    • A boundary point method to solve semidefinite programs
    • J. POVH, F. RENDL, AND A. WlEGELE, A boundary point method to solve semidefinite programs, Computing, 78 (2006), pp. 277-286
    • (2006) Computing , vol.78 , pp. 277-286
    • POVH, J.1    RENDL, F.2    WlEGELE, A.3
  • 31
    • 23844454333 scopus 로고    scopus 로고
    • New code upper bounds from the Terwilliger algebra and semidefinite programming
    • A. SCHRIJVER, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory, 51 (2005), pp. 2859-2866.
    • (2005) IEEE Trans. Inform. Theory , vol.51 , pp. 2859-2866
    • SCHRIJVER, A.1
  • 33
    • 0000009985 scopus 로고    scopus 로고
    • Coloring Hamming graphs, Optimal Binary Codes, and the 0/1-Borsuk Problem in Low Dimensions
    • Computational Discrete Mathematics, Springer-Verlag, Berlin
    • G. ZIEGLER, Coloring Hamming graphs, Optimal Binary Codes, and the 0/1-Borsuk Problem in Low Dimensions, in Computational Discrete Mathematics, Lecture Notes in Comput. Sci. 2122, Springer-Verlag, Berlin, 2001, pp. 159-171.
    • (2001) Lecture Notes in Comput. Sci , vol.2122 , pp. 159-171
    • ZIEGLER, G.1
  • 34
    • 67649490060 scopus 로고    scopus 로고
    • http://mat.gsia.cmu.edu/COLOR03/.
  • 35
    • 67649507723 scopus 로고    scopus 로고
    • http://infohost.nmt.edu/̃borchers/csdp.html.
  • 36
    • 67649456978 scopus 로고    scopus 로고
    • http://www-unix.mcs.anl.gov/̃benson/dsdp/.
  • 37
    • 67649504418 scopus 로고    scopus 로고
    • http://dollar.biz.uiowa.edu/̃burer/software/Max-AO/index.html.
  • 38
    • 67649473951 scopus 로고    scopus 로고
    • http://www.math.uni-klu.ac.at/or/Software/theta-bp.m.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.