Algorithmic Adventures - From Knowledge to Magic

What is an algorithm, what can we compute and what might we compute in the fu-ture? These are the questions which underline Hromkovič's book Algorithmic Adventures: From Knowledge to Magic. It covers a relatively broad range of topics, at an introductory overview level, which originated from a public lecture series at ETH Zürich (Swiss Federal Institute of Technology Zürich) in 2005. Given the general scope of informatics olympiads, it should be pointed out from the beginning that this is in no form an introductory algorithm text, such as Cormen et al [1] or Sedgewick [2]. This is not the place to find a description (or mention) of standard approaches such as dynamic programming or greedy algorithms, standard algorithms or mathematical foundations. Rather it provides an essentially recreational overview of algorithms – a style that introduces some fundamental concepts and glosses-over some technical details. The chapters within the book fit together well and tell an interesting story. Indeed, the structure of the book and the way in which the story flows between the chapters is one of the book's strengths. The book starts off by discussing scientific discipline, some basic logic and the notion of proof. We then lead in to the standard comparison of an algorithm and a recipe. This discussion is carried on in some depth, including discussions as to specificity of steps and non-termination. The story then moves to a discussion of the different types of infinity, which is then used to explain why some problems are unsolvable. At this point (almost half way through the book) complexity is introduced, along with a discussion of what is tractable. Random-ness is introduced next, along with witnesses and examples of how some hard problems can be solved with such algorithms.