Computing alignments with maximum synchronous moves via replay in coordinate planes

Optimal alignments are the basis of conformance checking. For long, researchers have been devoted to the efficiency issue of computing optimal alignments. This paper focuses on the optimality issue. Specifically, we aim to find alignments with maximum synchronous moves and minimum deviations. This paper introduces a coordinate-plane search space, which allows enumerating all the possible alignments. The alignments with maximum synchronous moves are translated into the lowest-cost paths, such that heuristic strategies (such as the Dijkstra algorithm) can be applied. Both theoretical proof and experimental results show that 100% optimality can be achieved.