Table 6.
Dominance relations for CALOT and SAT-based MaxSAT approaches for the Covering Array Number problem
| CALOT CCX a.0 | CALOT CCX a.1 | RC2-B CCX a.0 | RC2-B CCX a.0 wpm | linear CCX a.0 | loandra CCX a.0 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Size | Time | Size | Time | Size | Time | Size | Time | Size | Time | Size | Time | |
| W L | W L | W L | W L | W L | W L | W L | W L | W L | W L | W L | W L | |
| ACTS | 0 52 | 2 56 | 0 52 | 2 56 | 21 32 | 23 35 | 2 51 | 4 54 | 0 52 | 2 56 | 3 52 | 4 54 |
| CALOT CCX a.0 | – | – | 5 3 | 52 6 | 21 0 | 57 1 | 5 4 | 53 5 | 3 2 | 47 11 | 3 12 | 44 14 |
| CALOT CCX a.1 | – | – | – | – | 21 0 | 57 1 | 4 3 | 50 8 | 5 5 | 27 31 | 3 12 | 42 16 |
| RC2-B CCX a.0 | – | – | – | – | – | – | 0 19 | 31 25 | 0 21 | 1 57 | 2 20 | 3 54 |
| RC2-B CCX a.0 wpm | – | – | – | – | – | – | – | – | 3 5 | 7 51 | 2 11 | 8 49 |
| linear CCX a.0 | – | – | – | – | – | – | – | – | – | – | 3 11 | 41 17 |
| loandra CCX a.0 | – | – | – | – | – | – | – | – | – | – | – | – |
| loandra CCX a.1 | – | – | – | – | – | – | – | – | – | – | – | – |
| tt-open-wbo-inc CCX a.0 | – | – | – | – | – | – | – | – | – | – | – | – |
| tt-open-wbo-inc CCX a.1 | – | – | – | – | – | – | – | – | – | – | – | – |
| tt-open-wbo-inc CCX a.0 wpm | – | – | – | – | – | – | – | – | – | – | – | – |
| loandra CCX a.1 | tt-open-wbo-inc CCX a.0 | tt-open-wbo-inc CCX a.1 | tt-open-wbo-inc CCX a.0 wpm | tt-open-wbo-inc CCX a.1 wpm | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | time | size | time | size | time | size | time | size | time | |||
| W L | W L | W L | W L | W L | W L | W L | W L | W L | W L | |||
| ACTS | 3 52 | 4 54 | 1 52 | 2 56 | 0 53 | 1 57 | 1 52 | 2 56 | 0 53 | 1 57 | ||
| CALOT CCX a.0 | 3 12 | 44 14 | 1 13 | 13 45 | 0 13 | 12 46 | 2 12 | 15 43 | 0 12 | 19 39 | ||
| CALOT CCX a.1 | 3 11 | 42 16 | 1 12 | 9 49 | 0 13 | 6 52 | 1 10 | 7 51 | 0 11 | 11 47 | ||
| RC2-B CCX a.0 | 2 20 | 6 51 | 0 20 | 1 56 | 0 21 | 1 57 | 0 20 | 1 56 | 0 21 | 1 57 | ||
| RC2-B CCX a.0 wpm | 2 10 | 10 47 | 0 11 | 1 56 | 1 13 | 4 54 | 0 9 | 2 55 | 1 11 | 6 52 | ||
| linear CCX a.0 | 3 11 | 41 17 | 1 12 | 7 51 | 1 13 | 4 54 | 2 11 | 3 55 | 1 12 | 7 51 | ||
| loandra CCX a.0 | 2 7 | 38 17 | 4 5 | 9 48 | 4 7 | 9 49 | 5 3 | 12 45 | 3 5 | 10 48 | ||
| loandra CCX a.1 | – | – | 5 3 | 13 44 | 6 5 | 9 49 | 7 3 | 13 44 | 6 5 | 13 45 | ||
| tt-open-wbo-inc CCX a.0 | – | – | – | – | 2 3 | 39 19 | 4 2 | 38 19 | 2 4 | 42 16 | ||
| tt-open-wbo-inc CCX a.1 | – | – | – | – | – | – | 6 3 | 21 37 | 2 3 | 39 19 | ||
| tt-open-wbo-inc CCX a.0 wpm | – | – | – | – | – | – | – | – | 1 4 | 43 15 | ||
Bold values highlight winning algorithm per size or runtime