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Complexity
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2020
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Article
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Tab 3
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Research Article
Degree-Constrained
-
Minimum Spanning Tree Problem
Table 3
Numerical results obtained with
and
for random graphs using
and
.
#
Gaps
Opt
Time
LP
Time
Opt
Time
LP
Time
%
%
1
50
10
46.86
42
2.29
43.38
0.23
46.86
340
1.25
43.38
0.20
7.43
7.43
2
20
113.97
2161
16.65
109.46
0.25
113.97
999
11.42
109.46
0.27
3.96
3.96
3
30
204.35
116
1.67
197.61
0.19
204.35
2024
14.65
197.61
0.19
3.30
3.30
4
50
459.09
123
1.00
444.77
0.25
459.09
629
3.87
447.87
0.20
3.12
2.44
5
100
25
115.44
358
46.71
114.54
0.53
115.44
97
54.60
114.54
0.70
0.78
0.78
6
50
263.95
1243
73.63
261.02
0.51
263.95
668
77.50
261.02
0.75
1.11
1.11
7
75
454.44
459
143.16
449.51
0.55
454.44
525
111.53
449.51
0.67
1.08
1.08
8
100
749.75
24
22.56
728.70
2.29
749.75
0
40.36
734.84
0.59
2.81
1.99
9
200
50
162.55
479
3995.62
160.36
2.21
162.55
920
2835.21
160.36
3.29
1.35
1.35
10
100
378.43
479
2671.16
373.28
3.81
—
—
7200
373.28
3.68
1.36
—
11
150
652.86
479
2097.25
642.84
4.71
652.86
465
1663.29
642.84
3.49
1.53
1.53
12
200
1049.25
607
505.27
1030.04
30.11
1049.25
502
1490.46
1034.23
3.21
1.83
1.43
1
50
10
52.22
5
1.01
46.42
0.25
52.22
190
1.73
46.30
0.20
11.12
11.34
2
20
134.08
379
3.43
129.90
0.33
134.08
1515
21.95
129.71
0.20
3.12
3.26
3
30
240.30
235
7.35
239.32
0.28
240.30
736
19.08
239.32
0.20
0.41
0.41
4
50
564.37
488
20.20
557.48
0.28
564.37
1647
42.00
557.08
0.19
1.22
1.29
5
100
25
123.71
1067
248.12
121.55
1.50
123.71
1933
237.10
121.54
0.70
1.74
1.75
6
50
287.78
1676
632.83
285.35
2.84
287.78
857
356.21
285.31
0.81
0.84
0.86
7
75
529.56
0
8.88
529.31
3.23
529.56
1050
639.40
529.31
0.76
0.05
0.05
8
100
—
—
7200
914.60
4.13
—
—
7200
914.63
0.89
—
—
9
200
50
184.29
10
228.02
184.29
13.13
—
—
7200
184.29
3.81
0
—
10
100
—
—
7200
435.45
26.49
—
—
7200
435.45
6.61
—
—
11
150
—
—
7200
774.76
55.04
—
—
7200
774.76
6.62
—
—
12
200
1285.32
1045
1408.71
1284.58
94.68
—
—
7200
1284.58
4.15
0.06
—
—: no solution found.