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Using binary decision diagrams for constraint handling in combinatorial interaction testing
Constraints among test parameters often have substantial effects on the
performance of test case generation for combinatorial interaction testing. This
paper investigates the effectiveness of the use of Binary Decision Diagrams
(BDDs) for constraint handling. BDDs are a data structure used to represent and
manipulate Boolean functions. The core role of a constraint handler is to
perform a check to determine if a partial test case with unspecified parameter
values satisfies the constraints. In the course of generating a test suite,
this check is executed a number of times; thus the efficiency of the check
significantly affects the overall time required for test case generation. In
the paper, we study two different approaches. The first approach performs this
check by computing the logical AND of Boolean functions that represent all
constraint-satisfying full test cases and a given partial test case. The second
approach uses a new technique to construct a BDD that represents all
constraint-satisfying partial test cases. With this BDD, the check can be
performed by simply traversing the BDD from the root to a sink. We developed a
program that incorporates both approaches into IPOG, a well-known test case
generation algorithm. Using this program, we empirically evaluate the
performance of these BDD-based constraint handling approaches using a total of
62 problem instances. In the evaluation, the two approaches are compared with
three different constraint handling approaches, namely, those based on Boolean
satisfiability (SAT) solving, Minimum Forbidden Tuples (MFTs), and Constraint
Satisfiction Problem (CSP) solving. The results of the evaluation show that the
two BDD-based approaches usually outperform the other constraint handling
techniques and that the BDD-based approach using the new technique exhibits
best performance