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Complexity
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2020
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Article
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Tab 2
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Research Article
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