This monograph surveys the recent developments in the field of parallel approximability to combinatorial optimization problems. The book is designed not specifically as a textbook, but as a sedimentation of a great deal of research done on this specific topic. Accordingly, we do not include a collection of exercises, but throughout the text we comment about different open research problems in the field. The monograph can easily be used as a support for advanced courses in either parallel or sequential algorithms, or for a graduate course on the topic.

In Chapter 1, we motivate the topic of parallel approximability, using an example. In the same chapter we keep the reasoning at a very intuitive level, and we survey some of the techniques and concepts that will be assumed throughout the book, like randomization and derandomization. In Chapter 2 we give a formal presentation of algorithms for the Parallel Random Access Machines model. We survey some of the known results on sequential approximability, and introduce the basic definitions and classes used in the theory of Parallel Approximability. The core of the book, Chapters 3 to 7, forms a collection of paradigms to produce parallel approximations. The word “paradigm” has a different semantic from the one used by Kuhn, in the sense that we use paradigm as a particular property or technique that can be used to give approximations in parallel for a whole class of problems. Chapter 3 presents the use of extremal graph theory, to obtain approximability to some graph problems. Chapter 4 presents parallel approximability results for profit/cost problems using the rounding, interval partitioning and separation techniques.