Explaining Propagators for String Edit Distance Constraints

The computation of string similarity measures has been thoroughly studied in the scientific literature and has applications in a wide variety of different areas. One of the most widely used measures is the so called string edit distance which captures the number of required edit operations to transform a string into another given string. Although polynomial time algorithms are known for calculating the edit distance between two strings, there also exist NP-hard problems from practical applications like scheduling or computational biology that constrain the minimum edit distance between arrays of decision variables. In this work, we propose a novel global constraint to formulate restrictions on the minimum edit distance for such problems. Furthermore, we describe a propagation algorithm and investigate an explanation strategy for an edit distance constraint propagator that can be incorporated into state of the art lazy clause generation solvers. Experimental results show that the proposed propagator is able to significantly improve the performance of existing exact methods regarding solution quality and computation speed for benchmark problems from the literature.