This paper introduces two new combinatorial optimization problems involving strings, namely, the Chain Alignment Problem, and a multiple version of it, the Multiple Chain Alignment Problem. For the first problem, a polynomial-time algorithm using dynamic programming is presented, and for the second one, a proof of its $\mathcal{NP}$-hardness and in approximability are provided, jointly with the main ideas of three heuristics proposed for it. The three heuristics are assessed with simulated data and the applicability of both problems here introduced is attested by their good results when modeling the Gene Identification Problem.

中文翻译：

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链对齐问题

本文介绍了两个新的涉及字符串的组合优化问题，即链对齐问题，以及它的多个版本，即多重链对齐问题。对于第一个问题，提出了一种使用动态规划的多项式时间算法，对于第二个问题，提出了一种证明$\mathcal{NP}$提供了硬度和近似性，并为此提出了三种启发式方法的主要思想。这3种启发式方法是用模拟数据进行评估的，在对基因识别问题进行建模时，本文引入的两个问题的适用性都证明了它们的良好结果。