Mutant reduction evaluation: what is there and what is missing?

Background. Many mutation reduction strategies, which aim to reduce the number of mutants, have been proposed. Problem. It is important to measure the ability of a mutation reduction strategy to maintain test suite effectiveness evaluation. However, existing evaluation indicators are unable to measure the "order-preserving ability". Objective. We aim to propose evaluation indicators to measure the "order-preserving ability" of a mutation reduction strategy, which is important but missing in our community. Method. Given a test suite on a Software Under Test (SUT) with a set of original mutants, we leverage the test suite to generate a group of test suites that have a partial order relationship in fault detecting potential. When evaluating a reduction strategy, we first construct two partial order relationships among the generated test suites in terms of mutation score, one with the original mutants and another with the reduced mutants. Then, we measure the extent to which the two partial order relationships are consistent. The more consistent the two partial order relationships are, the stronger the Order Preservation (OP) of the mutation reduction strategy is, and the more effective the reduction strategy is. Furthermore, we propose Effort-aware Relative Order Preservation (EROP) to measure how much gain a mutation reduction strategy can provide compared with a random reduction strategy. Result. The experimental results show that OP and EROP are able to efficiently measure the "order-preserving ability" of a mutation reduction strategy. As a result, they have a better ability to distinguish various mutation reduction strategies compared with the existing evaluation indicators. Conclusion. We suggest, for the researchers, that OP and EROP should be used to measure the effectiveness of a mutant reduction strategy.