On Unknown Small Subsets and Implicit Measures: New Techniques for Parameterized Algorithms

Parameterized computation is a recently proposed alternative approach to dealing with NP-hard problems. Developing efficient parameterized algorithms has become a very active research area in the current research in theoretical computer science. In this paper, we investigate a number of new algorithmic techniques that were proposed and initiated by ourselves in our research in parameterized computation. The techniques have proved to be very useful and promising, and have led to improved parameterized algorithms for many well-known NP-hard problems.