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Complexity
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2020
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Article
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Tab 4
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Research Article
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.