Longest Common Subsequence in Sublinear Space

TL;DR

This paper introduces a novel polynomial-time algorithm for computing the longest common subsequence that operates in sublinear space, significantly reducing memory usage while maintaining polynomial time complexity.

Contribution

It presents the first polynomial-time algorithm for LCS that uses o(n) space, improving efficiency for large string comparisons.

Findings

Algorithm runs in O(n^3) time

Uses O(n log^{1.5} n / 2^{√log n}) bits of space

First sublinear-space polynomial-time LCS algorithm

Abstract

We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n \log^{1.5} n}{2^{\sqrt{\log n}}}\right)$ bits of space.