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Volumn 48, Issue 4, 2006, Pages 681-699

The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem

Author keywords

Dimensionality reduction; Fast mixing; Markov process; Second smallest eigenvalue; Semidefinite programming

Indexed keywords

COMPUTATIONAL GEOMETRY; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; MATHEMATICAL PROGRAMMING; OPTIMIZATION; PROBLEM SOLVING;

EID: 33746329499     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144504443821     Document Type: Article
Times cited : (136)

References (32)
  • 2
    • 0033295981 scopus 로고    scopus 로고
    • CSDP, a C library for semidefinite programming
    • B. Borchers, CSDP, a C library for semidefinite programming, Optim. Methods Softw., 11 (1999), pp. 613-623.
    • (1999) Optim. Methods Softw. , vol.11 , pp. 613-623
    • Borchers, B.1
  • 4
    • 11344275321 scopus 로고    scopus 로고
    • Fastest mixing Markov chain on a graph
    • S. Boyd, P. Diaconis, and L. Xiao, Fastest mixing Markov chain on a graph, SIAM Rev., 46 (2004), pp. 667-689.
    • (2004) SIAM Rev. , vol.46 , pp. 667-689
    • Boyd, S.1    Diaconis, P.2    Xiao, L.3
  • 5
    • 0004055894 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK, Available online from
    • S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, 2004. Available online from www.stanford.edu/~boyd/ cvxbook.
    • (2004) Convex Optimization
    • Boyd, S.1    Vandenberghe, L.2
  • 6
    • 0001066943 scopus 로고
    • On the optimal design of columns against buckling
    • S. J. Cox and M. L. Overton, On the optimal design of columns against buckling, SIAM J. Math. Anal., 23 (1992), pp. 287-325.
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 287-325
    • Cox, S.J.1    Overton, M.L.2
  • 7
    • 0033471383 scopus 로고    scopus 로고
    • Where best to hold a drum fast
    • S. J. Cox and P. X. Uhlig, Where best to hold a drum fast, SIAM J. Optim., 9 (1999), pp. 948-964.
    • (1999) SIAM J. Optim. , vol.9 , pp. 948-964
    • Cox, S.J.1    Uhlig, P.X.2
  • 8
    • 0030487036 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for finite Markov chains
    • P. Diaconis and L. Saloff-Coste, Logarithmic Sobolev inequalities for finite Markov chains, Ann. Appl. Probab., 6 (1996), pp. 695-750.
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 695-750
    • Diaconis, P.1    Saloff-Coste, L.2
  • 9
    • 84948892773 scopus 로고
    • Absolute algebraic connectivity of trees
    • M. Fiedler, Absolute algebraic connectivity of trees, Linear Multilinear Algebra, 26 (1990), pp. 85-106.
    • (1990) Linear Multilinear Algebra , vol.26 , pp. 85-106
    • Fiedler, M.1
  • 10
    • 38249003680 scopus 로고
    • Some minimax problems for graphs
    • M. Fiedler, Some minimax problems for graphs, Discrete Math., 121 (1993), pp. 65-74.
    • (1993) Discrete Math. , vol.121 , pp. 65-74
    • Fiedler, M.1
  • 12
    • 33749243862 scopus 로고    scopus 로고
    • Preprint 2005-12, Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany
    • F. Göring, C. Helmberg, and M. Wappler, Embedded in the Shadow of the Separator, Preprint 2005-12, Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany, 2005.
    • (2005) Embedded in the Shadow of the Separator
    • Göring, F.1    Helmberg, C.2    Wappler, M.3
  • 15
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
    • (1985) Matrix Analysis
    • Horn, R.1    Johnson, C.2
  • 16
    • 0030304775 scopus 로고    scopus 로고
    • Convex analysis on the Hermitian matrices
    • A. S. Lewis, Convex analysis on the Hermitian matrices, SIAM J. Optim., 6 (1996), pp. 164-177.
    • (1996) SIAM J. Optim. , vol.6 , pp. 164-177
    • Lewis, A.S.1
  • 17
    • 0042602157 scopus 로고    scopus 로고
    • Eigenvalue optimization
    • A. Lewis and M. Overton, Eigenvalue optimization, Acta Numerica, 5 (1996), pp. 149-190.
    • (1996) Acta Numerica , vol.5 , pp. 149-190
    • Lewis, A.1    Overton, M.2
  • 18
    • 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
  • 19
    • 0002676043 scopus 로고    scopus 로고
    • Some applications of Laplacian eigenvalues of graphs
    • in G. Hahn and G. Sabidussi, eds., NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 497, Kluwer, Dordrecht, The Netherlands
    • B. Mohar, Some applications of Laplacian eigenvalues of graphs, in Graph Symmetry: Algebraic Methods and Applications, G. Hahn and G. Sabidussi, eds., NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 497, Kluwer, Dordrecht, The Netherlands, 1997, pp. 227-275.
    • (1997) Graph Symmetry: Algebraic Methods and Applications , pp. 227-275
    • Mohar, B.1
  • 20
    • 14944353419 scopus 로고    scopus 로고
    • Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems
    • A. Nemirovski, Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems, SIAM J. Optim., 15 (2004), pp. 229-251.
    • (2004) SIAM J. Optim. , vol.15 , pp. 229-251
    • Nemirovski, A.1
  • 21
    • 0001110772 scopus 로고
    • On minimizing the maximum eigenvalue of a symmetric matrix
    • M. L. Overton, On minimizing the maximum eigenvalue of a symmetric matrix, SIAM J. Matrix Anal. Appl., 9 (1988), pp. 256-268.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 256-268
    • Overton, M.L.1
  • 22
    • 0003181133 scopus 로고
    • Large-scale optimization of eigenvalues
    • M. L. Overton, Large-scale optimization of eigenvalues, SIAM J. Optim., 2 (1992), pp. 88-120.
    • (1992) SIAM J. Optim. , vol.2 , pp. 88-120
    • Overton, M.L.1
  • 23
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • J. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optim. Methods Softw., 11-12 (1999), pp. 625-653.
    • (1999) Optim. Methods Softw. , vol.11-12 , pp. 625-653
    • Sturm, J.1
  • 24
    • 0033295027 scopus 로고    scopus 로고
    • SDPT3 - A MATLAB software package for semidefinite programming
    • K. Toh, M. Todd, and R. Tutuncu, SDPT3 - a MATLAB software package for semidefinite programming, Optim. Methods Softw., 11 (1999), pp. 545-581.
    • (1999) Optim. Methods Softw. , vol.11 , pp. 545-581
    • Toh, K.1    Todd, M.2    Tutuncu, R.3
  • 25
    • 0345530231 scopus 로고    scopus 로고
    • The Colin de Verdière graph parameter
    • in L. Lovász et al., eds., Bolyai Soc. Math. Stud. 7, János Bolyai Mathematical Society, Budapest
    • H. van der Holst, L. Lovász, and A. Schrijver, The Colin de Verdière graph parameter, in Graph Theory and Combinatorial Biology, L. Lovász et al., eds., Bolyai Soc. Math. Stud. 7, János Bolyai Mathematical Society, Budapest, 1999, pp. 29-85.
    • (1999) Graph Theory and Combinatorial Biology , pp. 29-85
    • van der Holst, H.1    Lovász, L.2    Schrijver, A.3
  • 26
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 30
    • 0009635625 scopus 로고    scopus 로고
    • SDPSOL: A parser/solver for semidefinite programs with matrix structure
    • in L. E. Ghaoui and S.-I. Niculescu, eds., SIAM, Philadelphia
    • S.-P. Wu and S. Boyd, SDPSOL: A parser/solver for semidefinite programs with matrix structure, in Advances in Linear Matrix Inequality Methods in Control, L. E. Ghaoui and S.-I. Niculescu, eds., SIAM, Philadelphia, 2000, pp. 79-91.
    • (2000) Advances in Linear Matrix Inequality Methods in Control , pp. 79-91
    • Wu, S.-P.1    Boyd, S.2
  • 31
    • 3142770678 scopus 로고    scopus 로고
    • Fast linear iterations for distributed averaging
    • L. Xiao and S. Boyd, Fast linear iterations for distributed averaging, Systems Control Lett., 53 (2004), pp. 65-78.
    • (2004) Systems Control Lett. , vol.53 , pp. 65-78
    • Xiao, L.1    Boyd, S.2
  • 32
    • 33747317125 scopus 로고    scopus 로고
    • Optimal scaling of a gradient method for distributed resource allocation
    • to appear in Available online from
    • L. Xiao and S. Boyd, Optimal scaling of a gradient method for distributed resource allocation, to appear in J. Optim. Theory Appl., 129 (2006). Available online from www.stanford.edu/~boyd/fast_redstb.
    • (2006) J. Optim. Theory Appl. , vol.129
    • Xiao, L.1    Boyd, S.2


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