Review of exact exponential algorithms by Fedor V. Fomin and Dieter Kratsch

It’s a well known fact of computational complexity theory that the vast majority of interesting algorithmic problems are, unfortunately, intractable. In other words, thanks to the theory of NPcompleteness, we know that for literally thousands of optimization problems it is impossible to obtain a polynomial-time algorithm that produces an exact solution (unless P=NP). Still, all these problems need to be solved, so what are we to do? The approach that has probably been most favored in the theoretical computer science community is to “approximate”, that is, try to design an efficient algorithm that gives a solution that is as good as possible. However, in many cases this is not appropriate, either because any sub-optimal solution is unacceptable or because even obtaining a decent approximate solution for our problem is hard. This is the motivation of this book, which deals with algorithms that always produce optimal solutions exact algorithms. Of course, assuming standard complexity assumptions, an algorithm that always produces optimal solutions for an NP-hard problem requires super-polynomial (usually exponential) time. In