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Tham khảo tài liệu 'simulation and the monte carlo method episode 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 310 COUNTING VIA MONTE CARLO Table 9.7 Performance of the PME algorithm for the random 3-SAT with the clause matrix A 75 X 325 and .V 100 000. t Mean If 1 Max Min Mean Found Max Min PV RE 6 0.00 0.00 0.00 0.00 0 0 0.0000 NaN 7 382.08 1818.15 0.00 4.70 35 0 0.0000 1.7765 8 1349.59 3152.26 0.00 110.30 373 0 0.0018 0.8089 9 1397.32 2767.18 525.40 467.70 1089 42 0.0369 0.4356 10 1375.68 1828.11 878.00 859.50 1237 231 0.1143 0.1755 11 1434.95 1776.47 1341.54 1153.70 1268 910 0.2020 0.0880 12 1374.64 1423.99 1340.12 1244.90 1284 1180 0.2529 0.0195 13 1392.17 1441.19 1356.97 1273.10 1290 1248 0.2770 0.0207 14 1397.13 1466.46 1358.02 1277.30 1291 1260 0.2816 0.0250 15 1384.37 1419.97 1354.32 1277.10 1296 1258 0.2832 0.0166 16 1377.75 1424.07 1320.23 1271.90 1284 1251 02870 0.0258 Figure 9.10 Typical dynamics of the PME algorithm for the random 3-SAT problem with the clause matrix A 75 X 325 and N 100 000. 0 iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiHiĩiữ 10 20 30 40 50 60 70 plullllllilljllllllllllllllllillllll.llillhllllllll.lllllhlllllllllillll 10 20 30 40 50 60 70 1 0.5 0 1 0.5 0 1 0.5 0 1 0.5 0 1 0.5 0 1 0.5 0 1 0.5 0 1 0.5 0 lllllll.lll II.lull lilii 1 Illi .11 Jill. -II.Ill lllhl 1 .III- 10 20 30 40 50 60 70 1 Illi 1111. 1 Lb Ln 1 _ .hll 1 . 1 1 1 1 1 .1 li 1 .11 li. 1 10 20 30 40 50 60 70 h II LlJ 1. 1 11 1. LI J 1 1 II 1 1 1 - 10 20 30 40 50 60 70 ._11 -h -1 1 L 1. 1. 1 II 1 - 10 20 30 40 50 60 70 .11 - 1 . 1 I 1 1. -hl 1 11 i r 10 20 30 40 50 60 70 .11 11 . 1 1 1. L 1 1 II 1 - 10 20 30 40 50 60 70 d 1 L 1 1. L 1 1 11 1 r 10 20 30 40 50 60 70 ._11 1 L 1 1. 111 II 1 II J_L 1 0 20 30 40 50 60 70 PROBLEMS 311 PROBLEMS 9.1 Prove the upper bound 9.21 . 9.2 Prove the upper bound 9.22 . 9.3 Consider Problem 8.9. Implement and run a PME algorithm on this synthetic maxcut problem for a network with n 400 nodes with m 200. Compare with the CE algorithm. 9.4 Let Al be an arbitrary collection of subsets of some finite set st. Show that uMi 52-52nAil 52
