Approximation Algorithms and the Hardness of Approximation (17w5133)

The Banff International Research Station will host the "Approximation Algorithms and the Hardness of Approximation" workshop from November 12th to November 17th, 2017.

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 P.not.=NP conjecture. 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.not.=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. Some of the
focus topics are:

- the Traveling Salesman Problem (TSP),
- the Unique Games Conjecture
- Graph routing and compressing

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides
an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional
de Ciencia y Tecnología (CONACYT).