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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Most of the many discrete optimization problems arising in the sciences, engineering, and mathematics are NP-hard, that is, there exist no efficient algorithms to solve them to optimality, assuming the conjecture that P does not equal NP. The area of approximation algorithms focuses on the design and analysis of efficient algorithms that find solutions that are within a guaranteed factor of the optimal one. Loosely speaking, in the context of studying algorithmic problems, an approximation guarantee captures the quality of an algorithm -- for every possible set of input data for the problem, the algorithm finds a solution whose cost is within this factor of the optimal cost. A hardness threshold indicates the difficulty of the algorithmic problem -- no efficient algorithm can achieve an approximation guarantee better than the hardness threshold assuming that P does not equal NP. Over the last two decades, there have been major advances on the design and analysis of approximation algorithms, and on the complementary topic of the hardness of approximation. The goal of the workshop is to focus on a few key topics that could lead to deep new results in the areas of approximation algorithms, combinatorial optimization, hardness of approximation, and proof complexity.

Physique mathématique,    Physique numérique