MOTIVATION: Searching the Longest Common Subsequences of many sequences is called a Multiple Longest Common Subsequence (MLCS) problem which is a very fundamental and challenging problem in many fields of data mining. The existing algorithms cannot be applicable to problems with long and large-scale sequences due to their huge time and space consumption. To efficiently handle large-scale MLCS problems, a Path Recorder Directed Acyclic Graph (PRDAG) model and a novel Path Recorder Algorithm (PRA) are proposed. RESULTS: In PRDAG, we transform the MLCS problem into searching the longest path from the Directed Acyclic Graph (DAG), where each longest path in DAG corresponds to an MLCS. To tackle the problem efficiently, we eliminate all redundant and repeated nodes during the construction of DAG, and for each node, we only maintain the longest paths from the source node to it but ignore all non-longest paths. As a result, the size of the DAG becomes very small, and the memory space and search time will be greatly saved. Empirical experiments have been performed on a standard benchmark set of both DNA sequences and protein sequences. The experimental results demonstrate that our model and algorithm outperform the related leading algorithms, especially for large-scale MLCS problems. AVAILABILITY AND IMPLEMENTATION: This program code is written by the first author and can be available at https://www.ncbi.nlm.nih.gov/nuccore and https://blog.csdn.net/wswguilin. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Strategic air traffic management (SATM) problem, one of the critical tasks in air traffic operations, faces new challenges as the increased concerns on environmental impact and operation efficiency of the air transportation, and the system uncertainty increases due to the time-varying interference, such as the convective weather. To effectively address these challenges, we propose the formulation and solution of a generalized 4-D SATM problem for an air traffic system with convective weather uncertainty. The proposed SATM problem formulation is computationally tractable and the schedule results can realize the avoidance of the convective weather with more than a tolerable risk probability. We provide a solution approach to tackle this problem with complex mathematical basics and illustrate the capabilities of the proposed mixed integer solution approach on the real regional air traffic system operated by the China civil aviation administration. Numerical results demonstrate the effectiveness of the proposed solution approach.