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

2026-08-14

AI Summary

This study addresses the problem of minimizing insertion-deletion costs in longest common subsequence alignment for run-length encoded strings. We propose a block-boundary dynamic programming algorithm that models run pairs as homogeneous blocks, employing explicit state transition functions while storing states exclusively at block boundaries to eliminate redundant computations. The proposed method achieves a time complexity of O(mN + nM) and a space complexity of O(nm). Compared to conventional approaches, this framework significantly enhances computational efficiency for compressed string alignment, offering an effective solution for processing large-scale repetitive sequence data.

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.

Problem

• Longest Common Subsequence
• Run-Length Encoded Strings
• Minimum Alignment Cost
• Tie-breaking Variant

Innovation

• Run-Length Encoding
• Longest Common Subsequence
• Block-Boundary Dynamic Programming
• Minimum Alignment Cost
• Transfer Function