Degree-Constrained -Minimum Spanning Tree Problem

Table 2

Numerical results obtained with and for Euclidean graphs using and .

#													Gaps
			Opt		Time	LP	Time	Opt		Time	LP	Time	%	%
1	Berlin52	10	274.46	10	2.25	253.21	0.34	274.46	60	0.94	253.21	0.28	7.74	7.74
2		20	926.77	543991	218.23	801.28	0.20	926.77	591996	300.65	801.28	0.19	13.54	13.54
3		30	1935.71	4246933	3600	1666.19	0.20	1935.71	5292832	3600	1666.19	0.19	13.92	13.92
4		52	6081.63	2024616	3600	5567.13	0.20	6081.63	1688601	3600	5567.13	0.19	8.46	8.46
5	gr96	25	74.14	488206	3600	40.18	0.41	74.14	452709	3600	40.18	0.39	45.81	45.81
6		50	163.11	513293	3600	117.66	0.55	162.80	462902	3600	117.66	0.42	27.86	27.73
7		75	269.15	593506	3600	222.47	0.48	269.23	672775	3600	222.47	0.41	17.34	17.37
8		96	436.65	1192367	3600	384.51	0.80	436.69	1168784	3600	384.51	0.70	11.94	11.95
9	ch150	50	1607.24	243342	3600	1258.47	0.95	1610.93	157353	3600	1258.47	0.94	21.70	21.88
10		80	2657.21	186474	3600	2303.05	1.01	2694.88	154768	3600	2303.05	0.90	13.33	14.54
11		100	3457.86	199914	3600	3058.71	0.97	3441.59	129318	3600	3058.71	0.92	11.54	11.13
12		150	5914.15	215787	3600	5522.97	0.95	5923.78	234887	3600	5522.97	0.89	6.61	6.77
1	Berlin52	10	279.23	0	0.52	261.79	0.30	279.23	0	0.53	261.79	0.22	6.25	6.25
2		20	1015.39	2253	7.08	862.04	0.25	1015.39	8735	15.91	862.04	0.22	15.10	15.10
3		30	2065.12	9446	12.21	1871.76	0.28	2065.12	543	9.36	1871.76	0.27	9.36	9.36
4		52	6968.77	1699	8.24	6545.08	0.27	6968.77	1244	7.44	6545.08	0.23	6.08	6.08
5	gr96	25	74.59	380670	3600	45.19	0.77	74.59	324849	3600	45.19	2.39	39.42	39.42
6		50	168.53	270415	3600	128.73	0.92	174.25	194752	3600	128.73	8.45	23.62	26.12
7		75	283.14	154838	3600	248.44	13.60	288.49	310429	3600	248.44	0.58	12.25	13.88
8		96	474.95	168539	3600	452.14	9.66	476.08	397540	3600	452.14	0.72	4.80	5.03
9	ch150	50	1753.83	98742	3600	1356.91	1.04	1807.83	86310	3600	1356.91	9.91	22.63	24.94
10		80	2917.72	73829	3600	2489.25	2.29	2881.72	60210	3600	2489.25	10.64	14.69	13.62
11		100	3744.47	66710	3600	3302.54	15.88	4013.58	54518	3600	3302.54	14.05	11.80	17.72
12		150	6411.73	62743	3600	6158.67	1.15	6397.12	70574	3600	6158.67	1.01	3.95	3.73