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New Approaches to Network Design

Final Report Summary - NEWNET (New Approaches to Network Design)

In this project we developed efficient algorithms to solve fundamental computational problems, either exactly or in an approximate sense, with a special focus on applications arising from network design, analysis and management. Among others, we developed algorithms to design cheap networks that are resilient to link failures. We also designed improved algorithms to schedule tasks in the presence of time-varying resources. Solving a 40 years old open problem, we developed the first subcubic algorithm for RNA-folding, one of the most relevant problems in computational biology.
On the negative side, we proved that, for some of these problems, "very" efficient algorithms do not exist. For example, under reasonable conjectures, there is no subcubic algorithm to find the most "central" node in a network, according to different notions of centrality. This shows that the existing algorithms (developed in the 60's and 70's) to do that are essentially best possible.