Reads will form a collection of strings Patterns that we wish to match against a reference genome Text. For each string in Patterns, we will first find all its exact matches as a substring of Text (or conclude that it does not appear in Text). When hunting for the cause of a genetic disorder, we can immediately eliminate from consideration areas of the reference genome where exact matches occur. We will later generalize this problem to find approximate matches, where single nucleotide substitutions in reads separate the individual from the reference genome (or represent errors in reads).

Multiple Pattern Matching Problem:Find all occurrences of a collection of patterns in a text. Input: A string Text and a collection Patterns containing (shorter) strings. Output: All starting positions in Text where a string from Patterns appears as a substring.

To solve this problem, we will consolidate Patterns into a directed tree called a trie (pronounced “try”), which is written Trie(Patterns) and has the following properties.

The trie has a single root node with indegree 0, denoted root.

Each edge of Trie(Patterns) is labeled with a letter of the alphabet.

Edges leading out of a given node have distinct labels.

Every string in Patterns is spelled out by concatenating the letters along some path from the root downward.

Every path from the root to a leaf, or node with outdegree 0, spells a string from Patterns.

The most obvious way to construct Trie(Patterns) is by iteratively adding each string from Patterns to the growing trie, as implemented by the following algorithm.

TRIECONSTRUCTION(Patterns) Trie ← a graph consisting of a single node root for each string Pattern in Patterns currentNode ← root fori ← 1 to |Pattern| if there is an outgoing edge from currentNode with label currentSymbol currentNode ← ending node of this edge else
add a new node newNode to Trie
add a new edge from currentNode to newNode with label currentSymbol currentNode ← newNode returnTrie

Trie Construction Problem

Construct a trie on a collection of patterns.

Given: A collection of strings Patterns.

Return: The adjacency list corresponding to Trie(Patterns), in the following format. If Trie(Patterns) has n nodes, first label the root with 1 and then label the remaining nodes with the integers 2 through n in any order you like. Each edge of the adjacency list of Trie(Patterns) will be encoded by a triple: the first two members of the triple must be the integers labeling the initial and terminal nodes of the edge, respectively; the third member of the triple must be the symbol labeling the edge.