Rethinking Basis Path Testing: Mixed Integer Programming Approach for Test Path Set Generation

• URL: http://arxiv.org/abs/2601.05463v1
• Date: Fri, 09 Jan 2026 01:36:29 GMT
• Title: Rethinking Basis Path Testing: Mixed Integer Programming Approach for Test Path Set Generation
• Authors: Chao Wei, Xinyi Peng, Yawen Yan, Mao Luo, Ting Cai,
• Abstract summary: This paper reframes basis path generation from a procedural search task into a declarative optimization problem.<n>We introduce a Mixed Programming (MIP) framework designed to produce a complete basis path set that is globally optimal in its structural simplicity.<n>Our framework includes two complementary strategies: a Holistic MIP model that guarantees a theoretically optimal path set, and a scalable Incremental MIP strategy for large, complex topologies.
• Score: 7.012302821190496
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Basis path testing is a cornerstone of structural testing, yet traditional automated methods, relying on greedy graph-traversal algorithms (e.g., DFS/BFS), often generate sub-optimal paths. This structural inferiority is not a trivial issue; it directly impedes downstream testing activities by complicating automated test data generation and increasing the cognitive load for human engineers. This paper reframes basis path generation from a procedural search task into a declarative optimization problem. We introduce a Mixed Integer Programming (MIP) framework designed to produce a complete basis path set that is globally optimal in its structural simplicity. Our framework includes two complementary strategies: a Holistic MIP model that guarantees a theoretically optimal path set, and a scalable Incremental MIP strategy for large, complex topologies. The incremental approach features a multi-objective function that prioritizes path simplicity and incorporates a novelty penalty to maximize the successful generation of linearly independent paths. Empirical evaluations on both real-code and large-scale synthetic Control Flow Graphs demonstrate that our Incremental MIP strategy achieves a 100\% success rate in generating complete basis sets, while remaining computationally efficient. Our work provides a foundational method for generating a high-quality structural "scaffold" that can enhance the efficiency and effectiveness of subsequent test generation efforts.

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