Introduction to Combinatorial Testing - Automatic Generation of Combinatorial Test Data - page 9

covered in the test suite. A seed can be specified by a set of parameter-value pairs, like
{ ( p i 1 , v i 1 ), ( p i 2 , v i 2 ),...,( p i l , v i l ) } .

In the rest of this topic, we use the term target combinations to denote parameter com-
binations, which need to be covered as specified by the coverage requirement (covering
strength or seeds).

1.4.2 Variable Strength Covering Arrays and Tuple Density

For CAs, the strength t is quite important. The larger it is, the more complete the testing
will be. However, as t becomes larger, the number of test cases may increase rapidly.
The original definition of CAs requires all t -way parameter combinations to be cov-
ered. However, there are many cases where some parameters interact more (or less) with
each other than with other parameters. If we enforce a global strength, the covering
strength needs to be set at the highest interaction level, which will greatly increase the
number of test cases, and a lot of resources will be wasted on testing unimportant para-
meter combinations. Cohen et al. [ 11 , 12 ] introduced the concept of variable strength
covering arrays (VCA), which allows the tester to specify different covering strengths
on different subsets of parameters.
Definition 1.5 A variable strength t + is a set of

coverage requirements, where P i is a set of parameters, and t i is a covering strength on
P i ,for1

={ ( P 1 , t 1 ), ( P 2 , t 2 ),...,( P l , t l )) }

≤ i ≤ l . Each requirement ( P i , t i ) requires that all t i -way value combinations

of parameters in P i be covered.
When we replace the (universal) strength t with a variable strength t + , the CA will
be called a variable strength covering array (VCA). Note that the previous definition of
strength t can be represented by a variable strength t + ={ ( { p 1 , p 2 ,..., p k } , t ) } . Thus,
the variable strength CA is a generalization of the (traditional) CA. On the other hand,
if a variable strength CA meets the covering requirement t + , then for each ( P i , t i ) ∈ t + ,
the subarray of parameters in P i is a CA of strength t i .
Figure 1.6 is an example of variable strength CAs. It is a CA of strength 2, except
that for the last 4 columns, the strength is 3.

2 1111
0 1000
1 0011
2 0100
1 1110
0 0101
2 1001
0 0010
1 1101
2 1011
2 0001
2 0111

3 1 2 4 2 4 Fig. 1.6 VCA ( 12 , , 2 , CA ( 12 , , 3 ))