Algorithmic complexity in computational biology: basics, challenges and limitations

Computational problems can be classified according to their algorithmic complexity, which is defined based on how the resources needed to solve the problem, e.g. the execution time, scale with the problem size. Many problems in computational biology are computationally infeasible in the sense that the exhaustive search for the optimal solution is prohibitive in practical terms. As a consequence, these problems are tackled through heuristics and approximations aiming to overcome the exceeding computational requirements at the cost of providing suboptimal solutions. The importance of defining the computational complexity of computational biology algorithms is a topic rarely surveyed for broad audiences of bioinformaticians and users of bioinformatics tools. However, recognizing the underlying complexity of any algorithm is essential for understanding their potential and limitations. Thus, the aim of this review is to survey the main algorithmic solutions to intractable problems in computational biology, highlighting the importance of High-Performance Computing in this area.