Single String

KMP

Knuth-Morris-Pratt, or KMP, is a linear time string comparison algorithm that matches prefixes. Specifically, it computes the longest substring that is both a prefix and suffix of a string, and it does so for every prefix of a given string.

Z Algorithm

The Z-Algorithm is another linear time string comparison algorithm like KMP, but instead finds the longest common prefix of a string and all of its suffixes.

Palindromes

Manacher

Manacher's Algorithm is functionally similarly to the Z-Algorithm and can compute information about palindromes. It can determine the longest palindrome centered at each character.

Palindromic Tree

A Palindromic Tree is a tree-like data structure that behaves similarly to KMP. Unlike KMP, in which the only empty state is $0$, the Palindromic Tree has two empty states: length $0$, and length $-1$. This is because appending a character to a palindrome increases the length by $2$, meaning a single character palindrome must have been created from a palindrome of length $-1$

Multiple Strings

Tries

A trie is a tree-like data structure that stores strings. Each node is a string, and each edge is a character. The root is the empty string, and every node is represented by the characters along the path from the root to that node. This means that every prefix of a string is an ancestor of that string's node.

Aho-Corasick

Aho-Corasick is the combination of trie and KMP. It is essentially a trie with KMP's "fail" array.