Longest Common Subsequence (Longest Common Subsequence)

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The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences).

Related Problems

Subproblem: Longest Common Substring with don't cares


$n$: length of the longer input string

$m$: length of the shorter input string

$r$: length of the LCS

$s$: size of the alphabet

$p$: the number of dominant matches (AKA number of minimal candidates), i.e. the total number of ordered pairs of positions at which the two sequences match

Table of Algorithms

Currently no algorithms in our database for the given problem.

Time Complexity Graph

Longest Common Subsequence - Time.png

Reductions FROM Problem

Problem Implication Year Citation Reduction
UOV If: to-time: $O((nm)^{({1}-\epsilon)})$, where $|x| = O(nd)$ and $|y| = O(md)$
Then: from-time: $O((nm)^{({1}-\epsilon/{2})})$
2015 https://arxiv.org/pdf/1502.01063.pdf link