Developing a Totally Unimodular Linear Program for Optimal Conformance Checking: When and Why It Complements A*

2026-05-26

AI Summary

This work addresses the exponential runtime overhead of the classical A* algorithm when handling long trajectories or those with substantial deviations. The authors reformulate alignment-based consistency checking as a totally unimodular linear programming (LP) problem over the synchronous product reachability graph, leveraging the underlying network flow structure to obtain integer-optimal solutions directly via LP relaxation—thus circumventing combinatorial optimization bottlenecks. This is the first application of totally unimodular LP to this task, revealing a complementary relationship between A* and LP-based approaches and enabling a high-accuracy algorithm selection strategy. Experiments on 2.1 million instances demonstrate that the LP method substantially accelerates computation on challenging trajectories, with a hybrid strategy achieving an average speedup of 38.6% and a selection accuracy of 96%.

Abstract

Alignment-based conformance checking is the state-of-the-art approach for comparing observed process executions with normative process models. The standard exact solution relies on an A*-based heuristic search, which can exhibit exponential runtime in the presence of long traces or substantial deviations. This paper introduces a reformulation of alignment-based conformance checking as a totally unimodular linear program (LP) defined on the reachability graph of the synchronous product. By exploiting the underlying network-flow structure, the proposed formulation guarantees the existence of an integral optimal extreme-point solution through LP relaxation, thereby avoiding the combinatorial overhead associated with integer variables and branch-and-bound search. We conduct an extensive empirical evaluation on more than 2.1 million conformance checking instances derived from real-world and synthetic benchmark datasets. The results show that A* and the LP approach exhibit complementary performance characteristics: the former performs best on short, well-conforming traces, while the LP formulation provides substantial speedups for longer traces with deviations, precisely where conformance checking is most informative. Based on these findings, we derive simple algorithm-selection guidelines that combine both approaches, achieving average runtime savings of 38.6% with 96% selection accuracy compared to always using A*.

Problem

• conformance checking
• alignment
• A* search
• long traces
• deviations

Innovation

• totally unimodular linear program
• conformance checking
• alignment
• A* search
• network flow