Degree-Constrained -Minimum Spanning Tree Problem

Table 4

Numerical results obtained with and for Euclidean graphs using and .

#													Gaps
			Opt		Time	LP	Time	Opt		Time	LP	Time	%	%
1	Berlin52	10	274.46	0	0.97	253.21	0.21	274.46	0	0.82	253.21	0.21	7.74	7.74
2		20	926.77	0	2.25	697.51	0.25	926.77	0	2.15	697.51	0.21	24.74	24.74
3		30	1935.71	175	2.31	1414.09	0.22	1935.71	427	6.12	1414.09	0.20	26.95	26.95
4		52	6081.63	556	2.00	4822.43	0.28	6081.63	95	2.20	4923.77	0.19	20.71	19.04
5	gr96	25	72.40	2518	268.87	38.47	0.51	72.40	913	301.42	38.47	0.61	46.87	46.87
6		50	162.80	3274	316.75	110.48	0.56	162.80	1816	250.78	110.46	0.60	32.14	32.15
7		75	267.57	591	109.28	210.19	1.86	267.57	615	157.00	210.18	0.68	21.44	21.45
8		96	436.23	480	70.35	354.60	3.72	436.23	985	42.30	357.83	0.60	18.71	17.97
9	ch150	50	1567.77	1734	921.27	1219.69	1.21	—	—	3600	1219.69	1.46	22.20	—
10		80	—	—	3600	2237.22	1.25	—	—	3600	2237.22	1.85	—	—
11		100	—	—	3600	2974.08	1.60	3399.17	1037	1009.76	2974.08	1.97	—	12.51
12		150	5882.45	982	212.27	5339.18	27.69	5882.45	974	245.39	5353.54	1.61	9.24	8.99
1	Berlin52	10	279.23	0	2.95	262.40	0.25	279.23	0	0.67	261.79	0.20	6.03	6.25
2		20	1015.39	1487	21.75	868.22	0.37	1015.39	84	3.21	862.04	0.19	14.49	15.10
3		30	2065.12	0	4.55	1874.56	0.34	2065.12	0	2.87	1871.76	0.22	9.23	9.36
4		52	6968.77	972	31.65	6554.14	0.28	6968.77	0	2.89	6545.08	0.20	5.95	6.08
5	gr96	25	73.56	1592	845.82	45.41	0.77	73.56	2525	621.64	45.19	0.62	38.27	38.57
6		50	168.53	862	299.41	129.00	2.81	168.53	601	350.55	128.73	0.67	23.46	23.62
7		75	283.14	1235	408.99	248.89	4.12	283.14	1672	447.78	248.44	0.64	12.10	12.25
8		96	474.95	2874	329.41	456.19	2.50	474.95	2482	315.00	452.14	0.56	3.95	4.80
9	ch150	50	—	—	3600	1358.73	16.52	—	—	3600	1356.91	2.46	—	—
10		80	3167.66	1241	3600	2491.52	22.79	—	—	3600	2489.25	2.34	21.35	—
11		100	5425.41	1224	3600	3306.74	20.47	—	—	3600	3302.54	2.79	39.05	—
12		150	7176.67	3698	3600	6166.49	29.53	—	—	3600	6158.67	1.78	14.08	—

—: no solution found.