Context sensitivity is a foundational technique in pointer analysis, critical and essential for improving precision but often incurring significant efficiency costs. Recent advances focus on selective context-sensitive analysis, where only a subset of program elements, such as methods or heap objects, are analyzed under context sensitivity while the rest are analyzed under context insensitivity, aiming to balance precision with efficiency. However, despite the proliferation of such approaches, existing methods are typically driven by specific code patterns, therefore lacking a comprehensive theoretical foundation for systematically identifying code scenarios that benefit from context sensitivity.

This paper presents a novel and foundational theory that establishes a sound over-approximation of the ground truth, i.e., objects that really improve precision under context sensitivity. The proposed theory reformulates the identification of this upper bound into graph reachability problems over a typical Pointer Flow Graph (PFG), each of which can be efficiently solved under context insensitivity, respectively. Building on this theoretical foundation, we introduce our selective context-sensitive analysis approach, Moon. Moon performs both backward and forward traversal on a Variable Flow Graph (VFG), an optimized variant of PFG designed to facilitate efficient traversal. This traversal systematically identifies all objects that improve precision under context sensitivity. Our theoretical foundation, along with carefully designed trade-offs within our approach, allows Moon to limit the scope of objects to be selected, leading to an effective balance between its analysis precision and efficiency. Extensive experiments with Moon across 30 Java programs demonstrate that Moon achieves 37.2X and 382.0X speedups for 2-object-sensitive and 3-object-sensitive analyses, respectively with negligible precision losses of only 0.1% and 0.2%. These results highlight that the balance between efficiency and precision achieved by Moon significantly outperforms all previous approaches.