3 times faster (> **3) than 2-way branching. Similarly for instances where each**
method was slower by < 1, < 2, and < **3 times compared to 2-way.**
Table 2 shows that although differences between methods can be quite large on single instances, the average differences between the most competitive methods are smaller. Dichotomic domain splitting is apparently the worst among the branching methods. However, it may fare better in problems with very large domain sizes4**. Excluding domain splitting, the other methods are usually no more**
that 2 times better or worse than 2-way branching on average. But there are cases where even the average differences are quite large.

The set branching methods, and especially the d**-way style ones, have slightly**
better or very close performance compared to 2-way branching on most classes. Also, these methods clearly outperform d**-way branching. Interestingly, the set** clustering methods are typically very competitive on the denser classes.

Table 3. **% categorization of all tried instances according to the performance of the**
branching methods compared to 2-way branching.

| d-way         | 2-way                                                 | d-way   | 2-way   |        |        |     |
|---------------|-------------------------------------------------------|---------|---------|--------|--------|-----|
| P roblem      | speedup d-way dom                                     | ties    | ties    | clust. | clust. |     |
| Class         | split set branch. set branch. set branch. set branch. |         |         |        |        |     |
| >1            | 29%                                                   | 11%     | 47%     | 68%    | 50%    | 45% |
| >2            | 8%                                                    | 0%      | 8%      | 2%     | 15%    | 16% |
| >3            | 2%                                                    | 0%      | 3%      | 0%     | 10%    | 6%  |
| <1            | 71%                                                   | 89%     | 53%     | 32%    | 50%    | 55% |
| <2            | 24%                                                   | 56%     | 21%     | 2%     | 21%    | 15% |
| <3            | 11%                                                   | 34%     | 6%      | 3%     | 11%    | 6%  |
| all instances |                                                       |         |         |        |        |     |

Table 3 shows that 2-way ties set branching is better than 2-way on **most**
instances. However, the margins are usually small. This is because the number of ties that occur during search is usually low, meaning that 2-way ties set branching often emulates the standard 2-way scheme. The other **set branching** methods are better than 2-way on roughly half of the instances. However, they can be significantly better, and worse, on quite a few.

| Mean                                       | SD          | t-value     | 95% C.I.      |               |
|--------------------------------------------|-------------|-------------|---------------|---------------|
| d-way                                      | -29.8 341.7 | -0.68       | (-116, 57)    |               |
| domain splitting                           | -241        | 456         | -4.1          | (-357, -125)  |
| d-way ties set branching                   | 9.48 326.3  | 0.23        | (-73.3, 92.3) |               |
| 2-way ties set branching                   | 31.7        | 234         | 1.06          | (-27.7, 91.1) |
| d-way clustering set branching 13.75 217.9 | 0.49        | (-41.6, 69) |               |               |
| 2-way clustering set branching             | 32.4 182.5  | 1.4         | (-13.9, 78.7) |               |

Table 4. **Paired t-test measurements for evaluation of the significance of the experimental results. 2-way branching is compared with the other branching schemes.**