The constrained longest common subsequence (CLCS) problem was introduced as a specific measure of similarity between molecules. It is a special case of the constrained sequence alignment problem and of the longest common subsequence (LCS) problem, which are both well-studied problems in the scientific literature. Finding similarities between sequences plays an important role in the fields of molecular biology, gene recognition, pattern matching, text analysis, and voice recognition, among others. The CLCS problem in particular represents an interesting measure of similarity for molecules that have a putative structure in common. This paper proposes an exact A^⁎ search algorithm for effectively solving the CLCS problem. This A^⁎ search is guided by a tight upper bound calculation for the cost-to-go for the LCS problem. Our computational study shows that on various artificial and real benchmark sets this algorithm scales better with growing instance size and requires significantly less computation time to prove optimality than earlier state-of-the-art approaches from the literature.

引入约束最长公共子序列（CLCS）问题作为分子之间相似性的特定度量。这是约束序列比对问题和最长公共子序列（LCS）问题的特例，它们都是科学文献中经过充分研究的问题。寻找序列之间的相似性在分子生物学，基因识别，模式匹配，文本分析和语音识别等领域中起着重要作用。对于具有共同假定结构的分子，CLCS问题尤其代表了一种有趣的相似性度量。本文提出了一种精确的^A⁎搜索算法来有效解决CLCS问题。该A ^⁎LCS问题的成本以严格的上限计算为指导。我们的计算研究表明，在各种人造基准和实际基准集合上，该算法可随着实例大小的增长而更好地扩展，并且与文献中较早的最新技术方法相比，其证明最佳性所需的计算时间明显更少。