Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 16

Comparison to results reported in [12] for the 𝐴 -algorithm. Columns 𝑀 𝐿 𝑆 𝑇 𝐸 𝐶 𝑛 list the average total running times for each group of this particular MIP in seconds, columns 𝐴 list the running times in seconds (rounded to integers) reported in [12], at which the best solution was found.

| 𝑉 | | 𝐿 | 𝑑 avg ( | 𝐿 𝑇 | ) 𝐴 M L S T E C t n opt | 𝑉 | | 𝐿 | 𝑑 avg ( | 𝐿 𝑇 | ) 𝐴 M L S T E C t n opt

100 25 0.8 1.8 0 0 10 400 100 0.8 2.0 n/a 60 10
100 25 0.5 2.0 0 0 10 400 100 0.5 2.2 n/a 61 10
100 25 0.2 4.5 0 0 10 400 100 0.2 5.8 (*) n/a NF 8
100 50 0.8 2.0 0 0 10 400 200 0.8 3.0 n/a 817 10
100 50 0.5 3.0 0 0 10 400 200 0.5 NA n/a NA NA
100 50 0.2 6.7 10 0 10 400 200 0.2 9.3 (*) n/a NF 0
100 100 0.8 3.0 0 2 10 400 400 0.8 n/a NF 0
100 100 0.5 4.7 2 9 10 400 400 0.5 6.2 (*) n/a NF 0
100 100 0.2 9.7 NF 6 10 400 400 0.2 14.6 (*) n/a NF 0
100 125 0.8 4.0 0 17 10 400 500 0.8 n/a NF 0
100 125 0.5 5.2 180 11 10 400 500 0.5 7.3 (*) n/a NF 0
100 125 0.2 11.0 NF 12 10 400 500 0.2 17.1 (*) n/a NF 0

200 50 0.8 2.0 0 3 10 500 125 0.8 2.0 0 157 10
200 50 0.5 2.2 0 2 10 500 125 0.5 2.6 0 196 10
200 50 0.2 5.2 5 10 10 500 125 0.2 6.3 (*) NF NF 2
200 100 0.8 2.6 0 28 10 500 250 0.8 3.0 5 2192 10
200 100 0.5 3.4 0 19 10 500 250 0.5 4.3 (*) NF NF 1
200 100 0.2 7.9 NF 191 10 500 250 0.2 10.3 (*) NF NF 0
200 200 0.8 4.0 23 911 10 500 500 0.8 4.8 (*) NF NF 0
200 200 0.5 NF NF 9 500 500 0.5 6.9 (*) NF NF 0
200 200 0.2 NF NF 7 500 500 0.2 16.4 (*) NF NF 0
200 250 0.8 4.0 21 301 10 500 625 0.8 5.1 (*) NF NF 0
200 250 0.5 NF NF 9 500 625 0.5 8.4 (*) NF NF 0
200 250 0.2 NF NF 3 500 625 0.2 19.0 (*) NF NF 0