"The main research goal of this project is the quest for rigorous mathematical theory explaining the power and failure of heuristics. The incapability of current computational models to explain the success of heuristic algorithms in practical computing is the subject of wide discussion for more than four decades. Within this project we expect a significant breakthrough in the study of a large family of heuristics: Preprocessing (data reduction or kernelization). Preprocessing is a reduction of the problem to a simpler one and this is the type of algorithms used in almost every application.As key to novel and groundbreaking results, the proposed project aims to develop new theory of polynomial time compressibility. Understanding the origin of compressibility will serve to build more powerful heuristic algorithms, as well as to explain the behaviour of preprocessing.The ubiquity of preprocessing makes the theory of compressibility extremely important.The new theory will be able to transfer the ideas of efficient computation beyond the established borders."