MacCorles: Minimum Alignment Cost Computation on Run-Length Encoded Strings

Abstract

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.