MacCorles：基于游程编码字符串的最小对齐代价计算
MacCorles: Minimum Alignment Cost Computation on Run-Length Encoded Strings
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中文总结 AI 辅助
该研究针对游程编码字符串提出平局破变体的最长公共子序列问题，设计了O(mN+nM)时间、O(nm)空间的块边界动态规划算法，用于最小化对齐代价。
中文摘要 AI 辅助
我们研究游程编码字符串上最长公共子序列问题的一种平局破变体。给定两个字符串，目标是首先像经典最长公共子序列问题一样最大化相等对齐字符对的数量，然后在所有此类对齐中最小化对齐长度，等价于在最大化相等对数量后最小化插入和删除的数量。我们证明该问题存在简单的块边界动态规划方案：若输入字符串长度为N和M，其游程编码分别有n和m个游程，该算法运行时间为O(mN+nM)，空间复杂度为O(nm)，算法将每对游程视为具有显式转移函数的同构块，仅在游程边界存储动态规划值。
英文摘要
We study a tie-breaking variant of the longest common subsequence problem on run-length encoded strings. Given two strings, the goal is first to maximize the number of equal aligned character pairs, as in the classical longest common subsequence problem, and then, among all such alignments, to minimize the alignment length. Equivalently, after maximizing the number of equal pairs, we minimize the number of insertions and deletions. We show that this problem admits a simple block-boundary dynamic program. If the input strings have lengths $N$ and $M$, and their run-length encodings have $n$ and $m$ runs, respectively, the algorithm runs in $O(mN+nM)$ time using $O(nm)$ space. The algorithm treats every pair of runs as a homogeneous block with an explicit transfer function and stores dynamic-programming values only on run boundaries.
