Deterministic Longest Common Subsequence Approximation in Near-Linear Time

TL;DR

This paper introduces a deterministic algorithm that approximates the Longest Common Subsequence in near-linear time with a sub-linear approximation ratio, marking a significant advancement in efficient sequence analysis.

Contribution

It presents the first deterministic near-linear time algorithm for LCS with a sub-linear approximation ratio, improving over previous randomized or less efficient methods.

Findings

Achieves an $O(n^{3/4} \, \log n)$ approximation ratio.

Runs in near-linear time, significantly faster than previous algorithms.

First deterministic approach with sub-linear approximation for LCS.

Abstract

We provide a deterministic algorithm that outputs an $O(n^{3/4} \log n)$-approximation for the Longest Common Subsequence (LCS) of two input sequences of length $n$ in near-linear time. This is the first deterministic approximation algorithm for LCS that achieves a sub-linear approximation ratio in near-linear time.