Effective-Resistance-Reducing Flows, Spectrally Thin Trees and Asymmetric TSP

We show that the integrality gap of the natural LP relaxation of the Asymmetric Traveling Salesman Problem is at most polyloglog(n). In other words, there is a polynomial time algorithm that approximates the value of the optimum tour within a factor of polyloglog(n). To prove this, we show that any k-edge-connected graph (for k=Omega(log(n))) has a polylog(k)/k thin tree. In this talk I will highlight the main ideas of our proof. This is a joint work with Nima Anari.

Speaker Details

Shayan Oveis Gharan is an assistant professor at CSE department at UW. He received his PhD from the MS&E department at Stanford University. His is mainly interested in the design and analysis of algorithms. In the past, he received several awards for his works on the Traveling Salesman Problem.

Series:
Microsoft Research Talks
Date:
Speakers:
Shayan Oveis-Gharan
Affiliation:
University of Washington

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Series: Microsoft Research Talks