메뉴 건너뛰기




Volumn 148, Issue 1, 2010, Pages 37-69

Gibbs rapidly samples colorings of G(n, d/n)

Author keywords

Colorings; Erdo double acute s R nyi random graphs; Gibbs samplers; Glauber dynamics; Mixing time

Indexed keywords


EID: 77953812471     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-009-0222-x     Document Type: Article
Times cited : (31)

References (25)
  • 1
    • 77953808271 scopus 로고    scopus 로고
    • Reversible Markov chains and random walks on graphs. (Book in preparation.) Current version online at
    • Aldous, D., Fill, J. A.: Reversible Markov chains and random walks on graphs. (Book in preparation.) Current version online at http://stat-www. berkeley. edu/users/aldous/book. html.
    • Aldous, D.1    Fill, J.A.2
  • 3
    • 85176687157 scopus 로고    scopus 로고
    • Bubley, R., Dyer, M.: Path coupling: a technique for proving rapid mixing in Markov chains. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS), pp. 223-231 (1997).
  • 4
    • 77953807428 scopus 로고    scopus 로고
    • Chen, M. F.: Trilogy of couplings and general formulas for lower bound of spectral gap. In: Probability towards 2000, number 128 in Lecture Notes in Statistics (1998).
  • 5
    • 33751507175 scopus 로고    scopus 로고
    • Randomly coloring sparse random graphs with fewer colors than the maximum degree
    • Dyer M., Flaxman A. D., Frieze A. M., Vigoda E.: Randomly coloring sparse random graphs with fewer colors than the maximum degree. Random Struct. Algorithms 29(4), 450-465 (2006).
    • (2006) Random Struct. Algorithms , vol.29 , Issue.4 , pp. 450-465
    • Dyer, M.1    Flaxman, A.D.2    Frieze, A.M.3    Vigoda, E.4
  • 6
    • 17744389641 scopus 로고    scopus 로고
    • Dyer, M., Frieze, A., Hayes, T., Vigoda, E.: Randomly coloring constant degree graphs. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS'04), pp. 582-589 (2004).
  • 7
    • 0033346853 scopus 로고    scopus 로고
    • Dyer, M., Frieze, A., Jerrum, M.: On counting independent sets in sparse graphs. In: Proceedings of 40th IEEE Sypmosium on Foundations of Computer Science (FOCS), pp. 210-217 (1999).
  • 8
    • 0003000289 scopus 로고    scopus 로고
    • On Markov chains for independent sets
    • Dyer M. E., Greenhill C. S.: On Markov chains for independent sets. J. Algorithms 35(1), 17-49 (2000).
    • (2000) J. Algorithms , vol.35 , Issue.1 , pp. 17-49
    • Dyer, M.E.1    Greenhill, C.S.2
  • 9
    • 77953811986 scopus 로고    scopus 로고
    • Efthymiou, C., Spirakis, P. G.: Randomly colouring sparse graphs using a constant number of colours (2007, unpublished).
  • 11
    • 46749137227 scopus 로고    scopus 로고
    • Gershchenfeld, A., Montanari, A.: Reconstruction for models on random graphs. In: Foundations of Computer Science, Annual IEEE Symposium, pp. 194-204. IEEE Computer Society (2007).
  • 12
    • 17744390398 scopus 로고    scopus 로고
    • Goldberg, L. A., Martin, R., Paterson, M.: Strong spatial mixing for lattice graphs with fewer colours. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS'04), pp. 562-571 (2004).
  • 13
    • 38049028708 scopus 로고    scopus 로고
    • Hayes, T. P.: A simple condition implying rapid mixing of single-site dynamics on spin systems. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), pp. 39-46 (2006).
  • 14
    • 84990721683 scopus 로고
    • A very simple algorithm for estimating the number of k-colorings of a low-degree graph
    • Jerrum M.: A very simple algorithm for estimating the number of k-colorings of a low-degree graph. Random Struct. Algorithms 7, 157-166 (1995).
    • (1995) Random Struct. Algorithms , vol.7 , pp. 157-166
    • Jerrum, M.1
  • 15
    • 0024904712 scopus 로고
    • Approximating the permanent
    • Jerrum M., Sinclair A.: Approximating the permanent. SIAM J. Comput. 18(6), 1149-1178 (1989).
    • (1989) SIAM J. Comput. , vol.18 , Issue.6 , pp. 1149-1178
    • Jerrum, M.1    Sinclair, A.2
  • 16
    • 4243139497 scopus 로고    scopus 로고
    • A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
    • Jerrum M., Sinclair A., Vigoda E.: A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries. J. ACM 51(4), 671-697 (2004).
    • (2004) J. ACM , vol.51 , Issue.4 , pp. 671-697
    • Jerrum, M.1    Sinclair, A.2    Vigoda, E.3
  • 17
    • 0035176101 scopus 로고    scopus 로고
    • Kenyon, C., Mossel, E., Peres, Y.: Glauber dynamics on trees and hyperbolic graphs. In: 42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001), pp. 568-578. IEEE Computer Soc., Los Alamitos, CA (2001).
  • 18
    • 77953810426 scopus 로고    scopus 로고
    • Martinelli, F.: Lectures on Glauber dynamics for discrete spin models. In: Lectures on Probability Theory and Statistics (Saint-Flour, 1997), vol. 1717 of Lecture Notes in Mathematics, pp. 93-191. Springer, Berlin (1999).
  • 19
    • 17744391844 scopus 로고    scopus 로고
    • Martinelli, F., Sinclair, A., Weitz, D.: The ising model on trees: boundary conditions and mixing time. In: Proceedings of the Forty Fourth Annual Symposium on Foundations of Computer Science, pp. 628-639 (2003).
  • 20
    • 58449101641 scopus 로고    scopus 로고
    • Mossel, E., Sly, A.: Rapid mixing of gibbs sampling on graphs that are sparse on average. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 238-247 (2008).
  • 21
    • 68349126915 scopus 로고    scopus 로고
    • Mossel, E., Sly, A.: Rapid mixing of gibbs sampling on graphs that are sparse on average. Random Struct. Algorithms (2009, to appear).
  • 22
    • 59449106512 scopus 로고    scopus 로고
    • On the hardness of sampling independent sets beyond the tree threshold
    • Mossel E., Weitz D., Wormald N.: On the hardness of sampling independent sets beyond the tree threshold. Prob. Theory Relat. Fields 143, 401-439 (2009).
    • (2009) Prob. Theory Relat. Fields , vol.143 , pp. 401-439
    • Mossel, E.1    Weitz, D.2    Wormald, N.3
  • 23
    • 0002730924 scopus 로고
    • Sequential and distributed graph coloring algorithms with performance analysis in random graph spaces
    • Shamir E., Upfal E.: Sequential and distributed graph coloring algorithms with performance analysis in random graph spaces. J. Algorithms 5(4), 488-501 (1984).
    • (1984) J. Algorithms , vol.5 , Issue.4 , pp. 488-501
    • Shamir, E.1    Upfal, E.2
  • 24
    • 1842498157 scopus 로고    scopus 로고
    • A note on the glauber dynamics for sampling independent sets
    • Vigoda E.: A note on the glauber dynamics for sampling independent sets. Electron. J. Comb. 8(1), 1-8 (2001).
    • (2001) Electron. J. Comb. , vol.8 , Issue.1 , pp. 1-8
    • Vigoda, E.1
  • 25
    • 33748095740 scopus 로고    scopus 로고
    • Weitz, D.: Counting indpendent sets up to the tree threshold. In: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, pp. 140-149. ACM (2006).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.