On the Use of Decision Diagrams for Finding Repetition-Free Longest Common Subsequences

We consider the repetition-free longest common subsequence (RFLCS) problem, where the goal is to find a longest sequence that appears as subsequence in two input strings and in which each character appears at most once. Our approach is to transform a RFLCS instance to an instance of the maximum independent set (MIS) problem which is subsequently solved by a mixed integer linear programming solver. To reduce the size of the underlying conflict graph of the MIS problem, a relaxed decision diagram is utilized. An experimental evaluation on two benchmark instance sets shows the advantages of the reduction of the conflict graphs in terms of shorter total computation times and the number of instances solved to proven optimality. A further advantage of the created relaxed decision diagrams is that heuristic solutions can be effectively derived. For some instances that could not be solved to proven optimality, new state-of-the-art results were obtained in this way.