A Space-Bounded Anytime Algorithm for the Multiple Longest Common Subsequence Problem

The multiple longest common subsequence (MLCS) problem, related to the identification of sequence similarity, is an important problem in many fields. As an NP-hard problem, its exact algorithms have difficulty in handling large-scale data and time-and space-efficient algorithms are required in real-world applications. To deal with time constraints, anytime algorithms have been proposed to generate good solutions with a reasonable time. However, there exists little work on space-efficient MLCS algorithms. In this paper, we formulate the MLCS problem into a graph search problem and present two space-efficient anytime MLCS algorithms, SA-MLCS and SLA-MLCS. SA-MLCS uses an iterative beam widening search strategy to reduce space usage during the iterative process of finding better solutions. Based on SA-MLCS, SLA-MLCS, a space-bounded algorithm, is developed to avoid space usage from exceeding available memory. SLA-MLCS uses a replacing strategy when SA-MLCS reaches a given space bound. Experimental results show SA-MLCS and SLA-MLCS use an order of magnitude less space and time than the state-of-the-art approximate algorithm MLCS-APP while finding better solutions. Compared to the state-of-the-art anytime algorithm Pro-MLCS, SA-MLCS and SLA-MLCS can solve an order of magnitude larger size instances. Furthermore, SLA-MLCS can find much better solutions than SA-MLCS on large size instances.