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.
[1] In most cases, a single input parameter or an interaction between two parameters is what causes a program's bugs.
[2] Bugs involving interactions between three or more parameters are both progressively less common [3] and also progressively more expensive to find, such testing has as its limit the testing of all possible inputs.
[4] 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.
[5] More rigorously, if we assume that a test case has
We note that the number of all possible test cases is a
Imagining that the code deals with the conditions taking only two parameters at a time, might reduce the number of needed test cases.
[clarification needed] To demonstrate, suppose there are X,Y,Z parameters.
We can use a predicate of the form
of order 3, which takes all 3 as input, or rather three different order 2 predicates of the form
can be written in an equivalent form of
{\displaystyle p_{xy}(X,Y),p_{yz}(Y,Z),p_{zx}(Z,X)}
where comma denotes any combination.
If the code is written as conditions taking "pairs" of parameters, then the set of choices of ranges
can be a multiset[clarification needed], because there can be multiple parameters having same number of choices.
is one of the maximum of the multiset
The number of pair-wise test cases on this test function would be:-
then the number of tests is typically O(nm), where n and m are the number of possibilities for each of the two parameters with the most choices, and it can be quite a lot less than the exhaustive
· N-wise testing can be considered the generalized form of pair-wise testing.
[citation needed] The idea is to apply sorting to the set
and call it the pairwise testing.
Generalizing further we can take the set
and call it the 3-wise testing.
T-wise testing.
The N-wise testing then would just be, all possible combinations from the above formula.
Consider the parameters shown in the table below.
'Enabled', 'Choice Type' and 'Category' have a choice range of 2, 3 and 4, respectively.
Multiplying the two largest values (3 and 4) indicates that a pair-wise tests would involve 12 tests.
The pairwise test cases, generated by Microsoft's "pict" tool, are shown below.