In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system (typically, a software algorithm), tests all possible discrete combinations of those parameters. Using carefully chosen test vectors, this can be done much faster than an exhaustive search of all combinations of all parameters, by "parallelizing" the tests of parameter pairs.
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Rationale
The most common bugs in a program are generally triggered by either a single input parameter or an interaction between pairs of parameters. Bugs involving interactions between three or more parameters are both progressively less common and also progressively more expensive to find---such testing has as its limit the testing of all possible inputs. Thus, a combinatorial technique for picking test cases like all-pairs testing is a useful cost-benefit compromise that enables a significant reduction in the number of test cases without drastically compromising functional coverage.
More rigorously, if we assume that a test function has
To demonstrate, suppose there are X,Y,Z parameters. We can use a predicate of the form
Therefore, if the
N-wise testing
N-wise testing can be considered the generalized form of pair-wise testing.
The idea is to apply sorting to the set
Now we can take the set
The N-wise testing then would just be, all possible combinations from the above formula.
Example
Consider the parameters shown in the table below.
'Enabled', 'Choice Type' and 'Category' have a choice range of 2, 3 and 4, respectively. An exhaustive test would involve 24 tests (2 x 3 x 4). Multiplying the two largest values (3 and 4) indicates that a pair-wise tests would involve 12 tests. The pict tool generated pairwise test cases is shown below.