Develop an efficient path finding algorithm for very large graphs

Abstract

Graphs are a data structure made of edges and nodes and both of them can be labelled by sequence, so that it is commonly used to represent a set of sequences, especially for some complex sequence like genome which makes up with a sequence of different proteins. Different sets of genome sequences may have some similar parts, by making use of the properties of the graph, a large graph can represent many combinations of genome sequences and each path in the graph spells a concatenated sequence, which reduces the redundancy part between each sequence. Besides, having an efficient way to accomplish align sequencing reads is very important for analysing genome assembly. In the project. I compared different data structures and algorithms related to graphs and familiar with different kinds of graph structures such as directed acyclic graphs and cyclic graphs. After that, I implemented a data structure to have a sequence analysis on a large graph such as retrieving the sequence from the graph by using a path. I have also developed two algorithms that can accomplish the align sequencing reads which including is sequence-to-graph matching and semi-global sequence-to-graph alignment by considering the time complexity. For the sequence-to-Graph Matching, the algorithm that I developed provide a time complexity O(|M||E|) to solve the problem, and for the sequence-to-Graph Alignment, the second algorithm I developed provide a time complexity O((|V|+|M|)|E|) to retrieve a path. (where |M| is the length of the searching sequence, |E| and |V| are the number of edges and nodes in the graph respectively.)