In computer science, a longest common substring of two or more strings is a longest string that is a substring of all of them. There may be more than one longest common substring. Applications include data deduplication and plagiarism detection.

Unlike the longest common subsequence problem, which finds insertions or deletions within the common text, the longest common substring problem seeks a contiguous substring shared by both texts.

The picture shows two strings where the problem has multiple solutions. Although the substring occurrences always overlap, it is impossible to obtain a longer common substring by "uniting" them.

The strings "ABABC", "BABCA" and "ABCBA" have only one longest common substring, viz. "ABC" of length 3. Other common substrings are "A", "AB", "B", "BA", "BC" and "C".

Given two strings, ${\displaystyle S}$ of length ${\displaystyle m}$ and ${\displaystyle T}$ of length ${\displaystyle n}$, find a longest string which is substring of both ${\displaystyle S}$ and ${\displaystyle T}$.

A generalization is the k-common substring problem. Given the set of strings ${\displaystyle S=\{S_{1},\ldots ,S_{K}\}}$, where ${\displaystyle |S_{i}|=n_{i}}$ and ${\textstyle \sum n_{i}=N}$. Find for each ${\displaystyle 2\leq k\leq K}$, a longest string which occurs as substring of at least ${\displaystyle k}$ strings.

One can find the lengths and starting positions of the longest common substrings of ${\displaystyle S}$ and ${\displaystyle T}$ in ${\displaystyle \Theta }$${\displaystyle (n+m)}$ time with the help of a generalized suffix tree. A faster algorithm can be achieved in the word RAM model of computation if the size ${\displaystyle \sigma }$ of the input alphabet is in ${\displaystyle 2^{o\left({\sqrt {\log(n+m)}}\right)}}$. In particular, this algorithm runs in ${\textstyle O\left((n+m)\log \sigma /{\sqrt {\log(n+m)}}\right)}$ time using ${\displaystyle O\left((n+m)\log \sigma /\log(n+m)\right)}$ space. Solving the problem by dynamic programming costs ${\displaystyle \Theta (nm)}$. The solutions to the generalized problem take ${\displaystyle \Theta (n_{1}+\cdots +n_{K})}$ space and ${\displaystyle \Theta (n_{1}\cdots n_{K})}$ time with dynamic programming and take ${\displaystyle \Theta (n_{1}+\cdots +n_{K})}$ time with a generalized suffix tree.

The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string terminators, to become "ABAB$0", "BABA$1" and "ABBA$2". The nodes representing "A", "B", "AB" and "BA" all have descendant leaves from all of the strings, numbered 0, 1 and 2.