Final Activity Report Summary - PHASETRANS (Phase transitions in computational complexity and formal verification: towards generic and realistic approaches) This project dealt with applying methods from Statistical Physics to problems from Computer Science. This is an exciting area at the crossroads of the two disciplines that provides a great understanding of the reasons for which some of the problem take a long time when solved on a computer. Our research contributions comprised on one hand the theory of such phase transitions. We studied phenomena (such as 'clustering' of solutions, or 'first-order phase transitions') that have implications for the running time of several algorithms, and the extent to which they have. We developed notions of 'reducing' one problem to another, and offered examples of such reductions. We developed mathematical methods (based on concepts from Statistical Physics) to analyse the performance of several existing algorithms from the literature, and developed new ones. We studied the applicability of such methods to problems of practical impact such as dividing a network into two equal parts while cutting the minimum number of links (a problem that appears in parallel computing) and in problems of grouping a set of items into clusters in the most natural way (an approach from data analysis and mining known as correlation clustering).
