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technologyreview.com·2h ago
AI Research
arXiv CS.AI·May 27·5 min read
Developing a Totally Unimodular Linear Program for Optimal Conformance Checking: When and Why It Complements A*
TL;DR
Conformance checking—verifying whether observed process executions match expected process models—relies on A* search, which becomes slow on long traces or large deviations. Researchers reformulated this problem as a totally unimodular linear program (a mathematical optimization form solvable in polynomial time) on the synchronous product reachability graph.
✦ Why It Matters
Engineers can choose between A* and LP solvers for conformance checking based on trace length and deviation patterns to minimize runtime.
Key Takeaways
- Reformulate conformance checking as totally unimodular LP for polynomial-time exact solutions.
- Use LP solver when A* exhibits exponential behavior on long traces or large deviations.
- Construct LP on synchronous product reachability graph combining trace and model states.
- Evaluate both A* and LP approaches on your dataset to select faster solver per instance.
Full Summary
Conformance checking validates whether recorded business process executions align with normative process models—a critical task in process mining and compliance auditing. Current state-of-the-art uses A* heuristic search to find optimal alignments, but this algorithm exhibits exponential runtime when traces are long or deviate substantially from the model.
The paper reformulates alignment-based conformance checking as a totally unimodular linear program (an LP where the constraint matrix has special mathematical properties enabling exact polynomial-time solution via standard LP solvers). The approach constructs this LP on the reachability graph of the synchronous product—a combined state space representing both the observed trace and the process model simultaneously.
By exploiting total unimodularity, the method avoids A* search's exponential blowup on certain problem structures. Results demonstrate that the LP formulation complements A* by solving different instance classes efficiently, providing practitioners with multiple solver options depending on trace characteristics.