Table III.

TRMP lower-bounding results for subproblems of Case 17. The meaning of each column is, in order: (1) node number, (2) number of rotamers in the subproblem, (3) number of rotamer pairs in the subproblem, (4) time (sec) for TRMP convergence, (5) median rotamer lower bound when not using pair flags (rotlb₁), (5) percentage of rotamers such that rotlb₁ > U, (6) time (sec) for computing rotlb₁ for all rotamers, (7) median rotamer-pair lower bound (rplb), (8) percentage of rotamer pairs such that rplb > U, (9) time (sec) for computing rplb for all rotamer pairs, (10) median rotamer lower bound when using pair flags (rotlb₂) after rotamer pairs were flagged by rplb, (11) percentage of rotamers such that rotlb₂ > U, (12) time (sec) for computing rotlb₂ for all rotamers. In the Table, time for TRMP convergence was excluded from time for computing rotlb₁, rotlb₂ or rplb. The value of U is −55.13, which is equal to the optimal value and was available as a global upper bound for each node in the table by the time they were expanded.

Node	#rots	#pairs	TTR	Rot lb’s w/o p-flags			Rot-pair lb’s			Rot lb’s w/p-flags
				med	%el	time	med	%el	time	med	%el	time
2	4504	8.4E6	148	−71.69	11	0	−40.21	74	1162	−70.91	26	7
4	3837	6.3E6	203	−70.98	9	0	−46.18	68	774	−70.61	21	3
6	3570	5.4E6	238	−80.98	3	0	−53.45	54	607	−80.56	7	4
8	3269	4.5E6	190	−84.57	1	1	−58.82	44	463	−84.35	3	1
10	2969	3.7E6	99	−73.98	12	0	−47.80	62	353	−73.59	17	2
12	2704	3.1E6	105	−84.00	7	0	−59.17	45	261	−83.81	8	1
14	2504	2.6E6	77	−84.10	13	0	−51.16	50	202	−83.93	14	1
16	2173	2.0E6	65	−82.25	5	0	−61.36	42	138	−82.13	8	0
18	1878	1.5E6	71	−88.56	5	0	−66.31	40	92	−88.47	9	0
20	1725	1.3E6	16	−86.09	7	0	−65.68	38	74	−85.94	8	0