Final Report Summary - ALUNIF (Algorithms and Lower Bounds: A Unified Approach)
The project proposed a unified approach to algorithms and lower bounds, by using existing connections between the two areas to arrive at new results in both, and also to develop stronger connections between these areas. These objectives were fully achieved. Various new and non-trivial algorithms for NP-hard problems were designed and analyzed, inspired by complexity-theoretic ideas, and algorithmic ideas were useful in several instances to show new complexity lower bounds. In addition, stronger connections between lower bounds and algorithms were established in the context of satisfiability, as well as in the context of learning. It was demonstrated that the connections between algorithms and lower bounds go even deeper than previously suspected, and that the study of the Minimum Circuit Size Problem is useful in gaining an understanding of this broader picture. The work on the project has resulted not only in progress towards strong complexity lower bounds using novel perspectives such as hardness magnification, but also a better understanding of barriers in the way of such progress.