Iterative Compression for Exactly Solving NP-Hard Minimization Problems

We survey the conceptual framework and several applications of the iterative compression technique introduced in 2004 by Reed, Smith, and Vetta. This technique has proven very useful for achieving a number of recent breakthroughs in the development of fixed-parameter algorithms for NP-hard minimization problems. There is a clear potential for further applications as well as a further development of the technique itself. We describe several algorithmic results based on iterative compression and point out some challenges for future research.