This work is licensed under a Creative Commons Attribution 4.0 International License. In reference [1] an overview of algorithms for this and similar problems in combinatorial group testing is provided.
In references [3,4] a general constraint-based approach is presented along with values of CAN(3,k,2) and CAN(4,k,2) (see Table below). The constraint model uses the original Boolean matrix and the matrix of size ((k choose t) x b) with variables in {0,..,g^t - 1}. The requirement of having all numbers in {0,..,g^t - 1} in any t rows of the covering array is satisfied by posting global cardinality constraints on the rows of the second matrix. The consistency of values of the variables in both matrices is ensured by specialised channelling constraints. For search to be efficient lexicographic ordering constraints are posted on the original matrix.
| t | k | |||||||
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
| 3 | 8*(8) | 10*(12) | 12*(12) | 12*(13) | 12*(13) | 12*(18) | 12*(18) | 12*(18) |
| 4 | 16*(16) | 16*(24) | 21*(28) | - (38) | - (42) | - (50) | - (50) | - (-) |
Table. CAN(3,k,2) and CAN(4,k,2) from reference [3] compared (in parentheses) with upper bounds from reference [1]
This work is licensed under a Creative Commons Attribution 4.0 International License.