Efficient Heuristics and Exact Methods for Pairwise Interaction Sampling

2025-10-07

AI Summary

This paper addresses the pairwise interaction testing problem for configurable software systems (e.g., automotive software): finding a minimum configuration set that covers every pair of Boolean features at least once within a vast configuration space. We first establish that this problem is BH-hard—a novel theoretical result. To solve it, we propose an integrated framework combining propositional logic modeling, exact algorithms, and efficient heuristics, incorporating new pruning strategies and problem decomposition techniques. On public benchmarks, our approach achieves optimal solutions for instances involving up to 500 million feasible pairwise interactions—the first method to do so—overcoming a critical limitation of prior approaches, which fail to yield feasible solutions on such large-scale instances. Experimental results demonstrate substantial improvements over state-of-the-art methods in both solution quality and scalability.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Combinatorial Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We consider a class of optimization problems that are fundamental to testing in modern configurable software systems, e.g., in automotive industries. In pairwise interaction sampling, we are given a (potentially very large) configuration space, in which each dimension corresponds to a possible Boolean feature of a software system; valid configurations are the satisfying assignments of a given propositional formula $varphi$. The objective is to find a minimum-sized family of configurations, such that each pair of features is jointly tested at least once. Due to its relevance in Software Engineering, this problem has been studied extensively for over 20 years. In addition to new theoretical insights (we prove BH-hardness), we provide a broad spectrum of key contributions on the practical side that allow substantial progress for the practical performance. Remarkably, we are able to solve the largest instances we found in published benchmark sets (with about 500000000 feasible interactions) to provable optimality. Previous approaches were not even able to compute feasible solutions.

Problem

• Finding minimal configurations for pairwise feature testing
• Solving large-scale optimization in configurable software systems
• Providing efficient heuristics and exact methods for sampling

Innovation

• Exact methods solve large instances to optimality
• Heuristic approaches compute feasible solutions efficiently
• Proving BH-hardness provides new theoretical insights