Final Report Summary - OPTAPPROX (Strong Convex Relaxations with Optimal Approximation Guarantees)
Our research project addresses the central question of what can be efficiently computed. Specifically, our approach is motivated by the use of powerful techniques, such as convex relaxations, for designing better algorithms for fundamental optimization problems.
The proposed research has led to the development of new convex relaxations, better algorithms, and an increased understanding of the limitations of these techniques. Indeed, we have broken several decade-old barriers by developing improved algorithms for central clustering problems, traveling salesman problems, and allocation problems. In addition, we have further understood the power of linear programming relaxations for basic optimization problems such as the vertex cover problem.
Apart from this theoretical progress, the developed techniques have also found more applied applications. For example, we have used the techniques to obtain better algorithms for diversifying search results and to summarize data.
The proposed research has led to the development of new convex relaxations, better algorithms, and an increased understanding of the limitations of these techniques. Indeed, we have broken several decade-old barriers by developing improved algorithms for central clustering problems, traveling salesman problems, and allocation problems. In addition, we have further understood the power of linear programming relaxations for basic optimization problems such as the vertex cover problem.
Apart from this theoretical progress, the developed techniques have also found more applied applications. For example, we have used the techniques to obtain better algorithms for diversifying search results and to summarize data.