An Efficient Diagnosis Algorithm for Inconsistent Constraint Sets (2102.09005v1)

Abstract: Constraint sets can become inconsistent in different contexts. For example, during a configuration session the set of customer requirements can become inconsistent with the configuration knowledge base. Another example is the engineering phase of a configuration knowledge base where the underlying constraints can become inconsistent with a set of test cases. In such situations we are in the need of techniques that support the identification of minimal sets of faulty constraints that have to be deleted in order to restore consistency. In this paper we introduce a divide-and-conquer based diagnosis algorithm (FastDiag) which identifies minimal sets of faulty constraints in an over-constrained problem. This algorithm is specifically applicable in scenarios where the efficient identification of leading (preferred) diagnoses is crucial. We compare the performance of FastDiag with the conflict-directed calculation of hitting sets and present an in-depth performance analysis that shows the advantages of our approach.

• The paper introduces FastDiag, an efficient divide-and-conquer algorithm for diagnosing inconsistent constraint sets without requiring the full calculation of conflict sets.
• Empirical evaluations show that FastDiag offers significant performance advantages over traditional methods, particularly for computing preferred diagnoses, exhibiting logarithmic complexity in consistency checks.
• FastDiag's efficiency makes it highly suitable for real-time applications like interactive product configuration and automated recommendation systems, addressing a key need for faster diagnosis.

An Efficient Diagnosis Algorithm for Inconsistent Constraint Sets

The paper presents a divide-and-conquer based diagnosis algorithm, termed FastDiag, aimed at efficiently identifying minimal sets of faulty constraints in over-constrained problems. This approach is particularly suited for scenarios where the identification of preferred or leading diagnoses is critical, such as in interactive configuration applications, where time is of the essence.

Background and Motivation

In systems utilizing constraint-based technologies, inconsistencies can frequently arise. These inconsistences occur when, for instance, user requirements in a configuration session conflict with the established configuration knowledge base. Additionally, inconsistencies are often seen during the engineering phase when constraints must align with a set of test cases. Addressing such inconsistencies efficiently is of paramount importance for maintaining system usability and ensuring customer satisfaction.

Traditional methods for diagnosing such inconsistencies typically leverage the calculation of conflict sets and hitting set algorithms, often resulting in computational inefficiencies. The primary contribution of this paper is the introduction of the FastDiag algorithm, which eschews the need for calculating complete conflict sets, thereby offering computational improvements.

FastDiag Algorithm

FastDiag works by iteratively diagnosing over-constrained sets through a systematic divide-and-conquer approach. The key operations can be summarized as:

1. Consistency Checking: By examining subsets of constraints, FastDiag determines whether the removal of certain constraints can resolve inconsistencies.
2. Recursive Division: The algorithm recursively divides the problem into smaller subsets to identify which constraints must be removed to restore consistency.
3. Diagnosis Preference: It adheres to a predefined lexicographical ordering of constraints, ensuring that diagnoses align with user preferences. This is crucial in applications where users have preferences for maintaining certain constraints over others.

Evaluation and Results

The performance of FastDiag has been compared against the traditional hitting set algorithm in combination with the QuickXplain conflict detection algorithm. The paper's empirical evaluations demonstrate that FastDiag provides a clear performance advantage, especially when calculating preferred diagnoses. Key results include:

• FastDiag achieves logarithmic complexity in terms of consistency checks required to calculate diagnoses.
• In various test scenarios, FastDiag outperformed traditional approaches in terms of runtime, particularly in interactive settings where calculating only the topmost preferred diagnoses is necessary.

Implications and Future Developments

The introduction of FastDiag has significant implications for the efficiency of constraint-based systems. Its ability to compute diagnoses swiftly makes it suitable for real-time applications such as online product configuration and automated recommendation systems.

Potential future developments include the algorithm's extension to support anytime diagnosis tasks and the exploration of its application in personalized recommendation systems, where the user-specific ranking of diagnoses could enhance user experience. Further empirical studies across different domains will be critical to validate FastDiag's applicability in diverse real-world scenarios.

Overall, the FastDiag algorithm represents a substantial advancement in the field of model-based diagnosis, providing a robust solution for managing inconsistent constraint sets in both theoretical and practical applications.