Page 190 - 《软件学报》2026年第4期
P. 190

陈小羽 等: 吉布斯采样在临界点前的快速收敛                                                          1631


                     54th Annual ACM SIGACT Symp. on Theory of Computing. Rome: ACM, 2022. 1418–1430. [doi: 10.1145/3519935.3520048]
                  [6]   Anari N, Liu KK, Gharan SO. Spectral independence in high-dimensional expanders and applications to the hardcore model. In: Proc. of
                     the 61st IEEE Annual Symp. on Foundations of Computer Science (FOCS). Durham: IEEE, 2020. 1319–1330. [doi: 10.1109/FOCS46700.
                     2020.00125]
                  [7]   Chen XY, Feng WM, Yin YT, Zhang XY. Optimal mixing for two-state anti-ferromagnetic spin systems. In: Proc. of the 63rd IEEE
                     Annual Symp. on Foundations of Computer Science (FOCS). Denver: IEEE, 2022. 588–599. [doi: 10.1109/focs54457.2022.00062]
                  [8]   Chen ZC, Liu KK, Vigoda E. Rapid mixing of Glauber dynamics up to uniqueness via contraction. In: Proc. of the 61st IEEE Annual
                     Symp. on Foundations of Computer Science (FOCS). Durham: IEEE, 2020. 1307–1318. [doi: 10.1109/FOCS46700.2020.00124]
                  [9]   Chen ZC, Liu KK, Vigoda E. Optimal mixing of Glauber dynamics: Entropy factorization via high-dimensional expansion. In: Proc. of
                     the 53rd Annual ACM SIGACT Symp. on Theory of Computing. ACM, 2021. 1537–1550. [doi: 10.1145/3406325.3451035]
                 [10]   Dyer M, Sinclair A, Vigoda E, Weitz D. Mixing in time and space for lattice spin systems: A combinatorial view. Random Structures &
                     Algorithms, 2004, 24(4): 461–479. [doi: 10.1002/rsa.20004]
                 [11]   Efthymiou C, Hayes TP, Štefankovič D, Vigoda E, Yin YT. Convergence of MCMC and loopy BP in the tree uniqueness region for the
                     hard-core model. SIAM Journal on Computing, 2019, 48(2): 581–643. [doi: 10.1137/17M1127144]
                 [12]   Hayes TP, Vigoda E. Coupling with the stationary distribution and improved sampling for colorings and independent sets. The Annals of
                     Applied Probability, 2006, 16(3): 1297–1318. [doi: 10.1214/105051606000000330]
                 [13]   Luby M, Vigoda E. Approximately counting up to four (extended abstract). In: Proc. of the 29th Annual ACM Symp. on Theory of
                     Computing. El Paso: ACM, 1997. 682–687. [doi: 10.1145/258533.258663]
                 [14]   Luby M, Vigoda E. Fast convergence of the Glauber dynamics for sampling independent sets. Random Structures & Algorithms, 1999,
                     15(3-4): 229–241. [doi: 10.1002/(SICI)1098-2418(199910/12)15:3/4<229::AID-RSA3>3.0.CO;2-X]
                 [15]   Sly  A.  Computational  transition  at  the  uniqueness  threshold.  In:  Proc.  of  the  51st  IEEE  Annual  Symp.  on  Foundations  of  Computer
                     Science. Las Vegas: IEEE, 2010. 287–296. [doi: 10.1109/FOCS.2010.34]
                 [16]   Vigoda E. A note on the Glauber dynamics for sampling independent sets. The Electronic Journal of Combinatorics, 2001, 8(1): R8. [doi:
                     10.37236/1552]
                 [17]   Weitz D. Counting independent sets up to the tree threshold. In: Proc. of the 38th Annual ACM Symp. on Theory of Computing. Seattle:
                     ACM, 2006. 140–149. [doi: 10.1145/1132516.1132538]
                 [18]   Greenhill C. The complexity of counting colourings and independent sets in sparse graphs and hypergraphs. Computational Complexity,
                     2000, 9(1): 52–72. [doi: 10.1007/PL00001601]
                 [19]   Valiant LG. The complexity of enumeration and reliability problems. SIAM Journal on Computing, 1979, 8(3): 410–421. [doi: 10.1137/
                     0208032]
                 [20]   Patel V, Regts G. Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials. SIAM Journal
                     on Computing, 2017, 46(6): 1893–1919. [doi: 10.1137/16M1101003]
                 [21]   Peters H, Regts G. On a conjecture of Sokal concerning roots of the independence polynomial. Michigan Mathematical Journal, 2019,
                     68(1): 33–55. [doi: 10.1307/mmj/1541667626]
                 [22]   Jerrum MR, Valiant LG, Vazirani VV. Random generation of combinatorial structures from a uniform distribution. Theoretical Computer
                     Science, 1986, 43: 169–188. [doi: 10.1016/0304-3975(86)90174-X]
                 [23]   Alev VL, Lau LC. Improved analysis of higher order random walks and applications. In: Proc. of the 52nd Annual ACM SIGACT Symp.
                     on Theory of Computing. Chicago: ACM, 2020. 1198–1211. [doi: 10.1145/3357713.3384317]
                 [24]   Anari N, Liu KK, Gharan SO, Vinzant C. Log-concave polynomials II: High-dimensional walks and an FPRAS for counting bases of a
                     matroid.  In:  Proc.  of  the  51st  Annual  ACM  SIGACT  Symp.  on  Theory  of  Computing.  Phoenix:  ACM,  2019.  1–12.  [doi:  10.1145/
                     3313276.3316385]
                 [25]   Cryan M, Guo H, Mousa G. Modified log-Sobolev inequalities for strongly log-concave distributions. In: Proc. of the 60th IEEE Annual
                     Symp. on Foundations of Computer Science (FOCS). Baltimore: IEEE, 2019. 1358–1370. [doi: 10.1109/FOCS.2019.00083]
                 [26]   Bubley  R,  Dyer  M.  Path  coupling:  A  technique  for  proving  rapid  mixing  in  Markov  chains.  In:  Proc.  of  the  38th  Annual  Symp.  on
                     Foundations of Computer Science. Miami Beach: IEEE, 1997. 223–231. [doi: 10.1109/sfcs.1997.646111]
                 [27]   Chen MF. Trilogy of couplings and general formulas for lower bound of spectral gap. In: Accardi L, Heyde CC, eds. Probability Towards
                     2000. New York: Springer, 1998. 123–136. [doi: 10.1007/978-1-4612-2224-8_7]
                 [28]   Weitz D. Combinatorial criteria for uniqueness of Gibbs measures. Random Structures & Algorithms, 2005, 27(4): 445–475. [doi: 10.
                     1002/rsa.20073]
                 [29]   Feng WM, Guo H, Yin YT, Zhang CH. Rapid mixing from spectral independence beyond the boolean domain. In: Proc. of the 2021
   185   186   187   188   189   190   191   192   193   194   195