Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 13

Overview of all test instances from SET-I, SET-II, and SET-III and corresponding best formulations.
Set | 𝑉 | 𝑑 / | 𝐸 | | 𝐿 | 𝑎 Best formulation
Set-I 100 0.2 50 1 E C s n
100 E C s n , E C s n h
125 E C s n
0.550 E C s n , E C n , E C s n h
100 E C n , E C s n h
125 E C n , E C s n h
0.850 E C s n , E C n
100 E C n , E C s n h
125 E C s n , E C n , E C s n h
200 0.2 100 E C s n , E C s n h
200 E C s n
250 E C s n , E C s n h
0.5100 E C s n
200 E C s n
250 E C s n , E C s n h
0.8100 E C s n
200 E C s n , E C s n h
250 E C s n , E C s n h
Set-II 1000 4000 5 E C ∗ (several variants having same performance)
10 E C ∗ (several variants having same performance)
20 E C ∗ (several variants having same performance)
Set-III 100 0.05 1 / 4 ⋅ | 𝐸 | Several methods having same performance
3 / 4 ⋅ | 𝐸 | C E F 𝑡 𝑛
0.2 1 / 4 ⋅ | 𝐸 | E C t ̃ n
3 / 4 ⋅ | 𝐸 | D C u t t n c
0.5 1 / 4 ⋅ | 𝐸 | E C t ̃ n o
3 / 4 ⋅ | 𝐸 | E C t n c
0.05 1 / 4 ⋅ | 𝐸 | 2 E C ∗ (several variants having same performance)
3 / 4 ⋅ | 𝐸 | E C t ̃ n o b , E C t n c
0.2 1 / 4 ⋅ | 𝐸 | E C t ̃ n o b , E C t n h
3 / 4 ⋅ | 𝐸 | D C u t t ̃ n o b c
0.5 1 / 4 ⋅ | 𝐸 | E C t n o b
3 / 4 ⋅ | 𝐸 | E C t n o c
0.05 1 / 4 ⋅ | 𝐸 | 5Several methods having 𝑡 ≤ 0
3 / 4 ⋅ | 𝐸 | D C u t t ̃ n c
0.2 1 / 4 ⋅ | 𝐸 | E C t n
3 / 4 ⋅ | 𝐸 | D C u t t n c o
0.5 1 / 4 ⋅ | 𝐸 | E C t n , E C t n h
3 / 4 ⋅ | 𝐸 | E C t n o b , E C t n h
1 0 × 1 0 30 1 E C ∗ (several variants having same performance)
50 E C s n o b
80 D C u t s ̃ n o b (best relaxation)
2 0 × 2 0 30 E C s n , E C n
50 E C s n
80 D C u t t ̃ n (best relaxation)