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AbstractContext: As a fault-based testing technique, mutation testing is effective at evaluating the quality of existing test suites. However, a large number of mutants result in the high computational cost in mutation testing. As a result, mutant reduction is of great importance to improve the efficiency of mutation testing. Objective: We aim to reduce mutants for weak mutation testing based on the dominance relation between mutant branches. Method: In our method, a new program is formed by inserting mutant branches into the original program. By analyzing the dominance relation between mutant branches in the new program, the non-dominated one is obtained, and the mutant corresponding to the non-dominated mutant branch is the mutant after reduction. Results: The proposed method is applied to test ten benchmark programs and six classes from open-source projects.The experimental results show that our method reduces over 80% mutants on average, which greatly improves the efficiency of mutation testing. Conclusion: We conclude that dominance relation between mutant branches is very important and useful in reducing mutants for mutation testing.