A Basic Parameterized Complexity Primer

This article was prepared for Mike Fellows Festschrift for his 60th Birthday. Since many of the contributed articles revolve around the concept of parameterized complexity, it seems reasonable to give the reader a (short) primer to this area. It is not intended as a complete survey of this very broad area in its current state; rather it is intended to give a flavour of the techniques used and the directions taken. Whilst not doing the area justice, the basics of the techniques for proving tractability, establishing hardness, and the philosophy are given. The basics from this paper will be amplified by many other articles in this Festschrift. Much fuller accounts can be found in the books Downey-Fellows [DF98,DFta], Niedermeier [Nie06], Flum-Grohe [FG06], the two issues of the Computer Journal [DFL08] and the recent survey Downey-Thilikos [DTH11].