tailieunhanh - SIMULATION AND THE MONTE CARLO METHOD Episode 12

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 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 0 NaN 7 35 0 8 373 0 9 1089 42 10 1237 231 11 1268 910 12 1284 1180 13 1290 1248 14 1291 1260 15 1296 1258 16 1284 1251 02870 Figure 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 10 20 30 40 50 60 70 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 lilii 1 Illi .11 Jill. 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 Prove the upper bound . Prove the upper bound . Consider Problem . 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. Let Al be an arbitrary collection of subsets of some finite set st. Show that uMi 52-52nAil 52