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ACUITY Report Summary

Project ID: 617951
Funded under: FP7-IDEAS-ERC
Country: Netherlands

Mid-Term Report Summary - ACUITY (Algorithms for coping with uncertainty and intractability)

A major goal is theoretical computer science is to understand why certain problems are hard to solve and others are easy.
This understanding often leads to new algorithmic approaches that are also broadly applicable to various problems.
Another intriguing phenomenon is that we may know that some problem always has a good solution, but this proof of existence does not
give any algorithm to find such a solution. In this project, we have made substantial progress on these fronts. In particular,
we show how convex programming hierarchies, which is a very powerful tool but not well understood, to obtain optimum algorithms for finding
independent sets in sparse graphs and for breaking a long-standing barrier for a scheduling problem. Second, we solve a major open question
for finding an algorithm for a fundamental problem is discrepancy theory that matches so-called Banaszczyk's bound which was only known existentially before.

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