Table II.

Results of solving the non-“Limited DEE” cases with BroMAP and DEE/A* (cases solved by limited DEE are not presented). Columns (1) No.: case number, (2) Bro: BroMAP solution time in seconds, (3) DEE: DEE/A* solution time in seconds, (4) T-Br: total number of branchings (i.e. splits), (5) F-Br: number of branchings during the first depth-first dive, (6) Skew: skewness of the search tree defined as $\frac{(\mathit{number}of\mathit{low}-\mathit{subproblems}\mathit{split})}{(\mathit{total}\mathit{number}of\mathit{splits})-1}$, (7) F-Ub: U - OP T, i.e. difference between the upper bound from the first depth-first dive and the GMEC energy, (8) Leaf: Σ_i log₁₀ |R_i| of the node at the end of the first depth-first dive, (9) Rdctn: average reduction of Σ_i log₁₀ |R_i| during the first depth-first dive, i.e. (logconf-Leaf)/(F-Br), where logconf is defined in Table I, (10) RC: number of rotamer-contractions performed, (11) %DE: BroMAP time percentage used for DEE-gp, (12) %A*: BroMAP time percentage used for A*, (13) %TR: BroMAP time percentage used for TRMP. Note that columns 11 to 13 may not sum to 100% because of time spent on rotamer-contraction and overhead of using the branch-and-bound framework.

No.	Bro	DEE	T-Br	F-Br	Skew	F-Ub	Leaf	Rdctn	RC	%DE	%A*	%TR
2	2.6E3	3.1E4	31	25	0.90	0.49	30.7	2.12	36	42.8	0.3	56.3
3	2.4E3	2.3E4	31	26	0.93	0.49	27.7	2.55	32	46.2	0.6	52.6
4	2.8E3	1.3E4	23	23	1	0	33.7	3.01	0	43.9	0.3	55.5
5	2.7E3	2.1E4	26	26	1	0.55	27.4	3.12	0	37.2	0.4	62.2
9	1.2E2	4.8E2	3	3	1	0	27.6	1.93	0	8.9	74.1	17.0
10	4.6E2	1.3E3	13	10	0.75	0.37	26.9	1.02	74	7.6	70.4	14.4
11	5.7E3	3.5E4	109	17	0.81	0.36	26.2	0.85	663	3.8	78.9	11.2
15	2.9E2	3.5E2	0	0	NA	0	NA	NA	0	94.6	0.4	4.7
23	1.5E2	2.6E2	0	0	NA	0	NA	NA	0	86.7	0	12.6
24	3.2E2	3.1E2	4	4	1	0	25.3	4.33	0	62.3	15.1	21.6
25	2.9E2	1.2E3	0	0	NA	0	NA	NA	0	89.6	0	10.4
26	1.4E3	1.7E3	11	11	1	0.89	29.2	1.65	0	46.1	0.4	53.2
33	4.1E2	2.1E3	13	13	1	0	27.9	2.43	0	34.7	4.5	59.8
34	1.1E3	3.7E3	19	19	1	0	30.0	2.32	0	32.2	2.7	64.8
35	2.8E3	4.1E4	21	21	1	0	28.7	3.03	0	50.7	0.6	48.6
36	4.6E3	2.3E4	25	25	1	0	27.9	3.39	0	53.2	0.7	45.9
37	2.5E2	2.5E2	0	0	NA	0	NA	NA	0	76.0	2.4	21.2
44	2.2E2	3.8E1	8	6	0.71	0.54	28.2	1.87	17	8.2	75.5	14.1
45	8.8E2	2.0E2	8	8	1	0	26.2	5.16	8	48.6	23.8	25.4
49	3.3E2	5.0E2	4	4	1	0	19.8	1.63	0	51.1	11.5	37.5
50	1.2E3	1.1E3	7	7	1	0	22.3	3.44	12	72.2	7.0	17.1
51	5.7E4	2.8E5	666	25	0.85	0.58	27.6	1.03	5,656	16.7	21.2	41.8
57	4.6E1	2.7E2	0	0	NA	0	NA	NA	0	84.8	0	15.2
58	1.5E3	1.0E3	19	19	1	0	28.8	2.69	0	42.5	0.2	57.1
59	4.4E2	4.0E3	0	0	NA	0	NA	NA	0	70.6	0	29.1
60	1.5E4	4.6E4	32	32	1	0	37.3	2.46	0	30.1	0.1	69.7
65	4.6E3	1.7E3	15	15	1	0	22.7	5.09	0	61.9	0	37.8
66	7.7E3	2.4E3	15	15	1	0	33.9	5.15	0	67.2	0	32.6
Cases below were solved by BroMAP only.
12	2.0E5	NA	2773	23	0.82	7.11	26.2	0.88	3.9E4	6.0	59.1	20.1
16	3.5E3	NA	12	11	0.91	0	23.6	1.75	30	41.7	6.0	49.3
17	1.1E5	NA	298	21	0.84	3.35	26.7	0.77	2,576	17.7	28.1	32.7
27	8.0E3	NA	23	23	1	0	27.8	0.99	13	32.2	1.1	66.4
28	2.1E4	NA	175	25	0.91	0	28.0	0.99	1,168	23.8	8.5	57.9
38	1.4E4	NA	155	31	0.87	0.50	30.2	1.47	571	30.9	0.4	62.8
39	1.2E5	NA	572	43	0.85	0	27.4	1.50	4,791	30.4	0.1	58.4
40	1.8E5	NA	293	43	0.81	0	29.6	1.91	2,440	35.9	0	56.1
41	2.1E5	NA	364	41	0.85	0	33	2.66	2,771	34.2	0	57.5
46	5.0E5	NA	2675	36	0.69	8.28	27.8	1.44	1.4E5	18.8	18.8	35.3
61	2.8E4	NA	55	49	0.96	0.36	28.2	2.04	15	49.0	0	50.8
62	3.6E5	NA	232	58	0.88	0.27	30.1	1.84	1,119	43.5	0	50.2
63	1.1E5	NA	143	53	0.85	0.29	32.8	2.08	506	41.4	0	55.4
67	1.3E5	NA	37	37	1	0	35.6	2.82	0	51.5	0	48.5