One of the most important trends in computing sciences is the analysis and development of efficient algorithms. In fact, this direction has had a long and reputable tradition, with significant theoretical and practical results. The members of the Research Group have been active in the area for a long time, with algebraic and arithmetical algorithms, geometry, and database related computational and mathematical problems in the forefront of their interest. More recently they have also been active in some engineering applications of discrete mathematics. The common central motif of their research activities has always been a quest for efficient algorithms which have strong theoretical guarantees for their good performance.