Graphs,  Algorithms,  and  Complexity

Abstract

Graphs are widely used to model biological or other types of networks. In the first part of this chapter, we provide a dense review of graph theory in regard to biological networks. An algorithm is a set of instructions to solve a given problem. We introduce basic algorithmic concepts and methods such as greedy and divide and conquer strategies with emphasis on the commonly used approaches of dynamic programming and graph algorithms in bioinformatics. A number of basic graph algorithms are described in detail and special graph structures are also illustrated. Many problems in bioinformatics cannot be solved in polynomial time and for these tasks, approximation algorithms with proven approximation ratios to optimal solutions are preferred. However, in many cases there are no approximation algorithms known to date and heuristics which are commonsense methods shown to work for most of the input combinations are used. We provide a brief survey of complexity classes and these mentioned methods in the final part.