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

TL;DR

This paper introduces a novel Mixed Integer Programming framework for basis path testing, transforming the path generation process into an optimization problem to produce globally optimal, simple, and complete path sets, improving over traditional greedy algorithms.

Contribution

It presents a new MIP-based approach with holistic and incremental strategies for optimal basis path set generation, addressing limitations of existing graph-traversal methods.

Findings

Incremental MIP achieves 100% success in generating complete basis sets.

The approach is computationally efficient on large-scale graphs.

Provides a high-quality structural scaffold for testing.

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.