Mining multiple longest common subsequences (MLCS) from a set of sequences of three or more over a finite alphabet$\Sigma$(a classical NP-hard problem [1]) is an important task in many fields, e.g., bio-informatics, computational genomics, pattern recognition, information extraction, etc. Applications in these fields often involve generating very long sequences (length$\geq 10_{,}000)$, referred to as big sequences. However, both existing exact and approximate MLCS algorithms face severe challenges in handling big sequences due to the over-whelming size of their problem-solving graph model MLCS­-$DAG$(Directed Acyclic Graph), leading to the issue of memory explosion or extremely high time complexity.

Mining multiple longest common subsequences (MLCS) from a set of sequences of length three or more over a finite alphabet (a classical NP-hard problem) is an important task in many fields, e.g., bioinformatics, computational genomics, pattern recognition, information extraction, etc. Applications in these fields often involve generating very long sequences (length$\geqslant$10,000), referred to as big sequences. Despite efforts in improving the time and space complexities ofMLCSmining algorithms, both existing exact and approximate algorithms face challenges in handling big sequences due to the overwhelming size of their problem-solving graph modelMLCS-DAG(DirectedAcyclicGraph), leading to the issue of memory explosion or extremely high time complexity. To bridge the gap, this paper first proposes a new identification and deletion strategy for different classes of non-critical points in the mining ofMLCS, which are the points that do not contribute to theirMLCSs mining in theMLCS-DAG. It then proposes a newMLCSproblem-solving graph model, namely$DAG_{KP}$(a newMLCS-DAGcontaining onlyKeyPoints). A novel parallelMLCSalgorithm, calledKP-MLCS(KeyPoint basedMLCS), is also presented, which can mine and compress allMLCSs of big sequences effectively and efficiently. Extensive experiments on both synthetic and real-world biological sequences show that the proposed algorithmKP-MLCSdrastically outperforms the existing state-of-the-artMLCSalgorithms in terms of both efficiency and effectiveness.

Information in various applications is often expressed as character sequences over a finite alphabet (e.g., DNA or protein sequences). In Big Data era, the lengths and sizes of these sequences are growing explosively, leading to grand challenges for the classical NP-hard problem, namely searching for the Multiple Longest Common Subsequences (MLCS) from multiple sequences. In this paper, we first unveil the fact that the state-of-the-art MLCS algorithms are unable to be applied to long and large-scale sequences alignments. To overcome their defects and tackle the longer and large-scale or even big sequences alignments, based on the proposed novel problem-solving model and various strategies, e.g., parallel topological sorting, optimal calculating, reuse of intermediate results, subsection calculation and serialization, etc., we present a novel parallel MLCS algorithm. Exhaustive experiments on the datasets of both synthetic and real-world biological sequences demonstrate that both the time and space of the proposed algorithm are only linear in the number of dominants from aligned sequences, and the proposed algorithm significantly outperforms the state-of-the-art MLCS algorithms, being applicable to longer and large-scale sequences alignments.