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Better-Than-2 Approximations for Weighted Tree Augmentation

Series: Theory Seminar

Speaker: Dr. Vera Traub Post doctoral Researcher ETH Zurich (Switzerland)

Date/Time: Sep 10 16:00:00

Location: Microsoft Teams - ON-LINE

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The Weighted Tree Augmentation Problem (WTAP) is one of the most basic connectivity augmentation problems. It asks how to increase the edge-connectivity of a given graph from 1 to 2 in the cheapest possible way by adding some additional edges from a given set. There are many standard techniques that lead to a 2-approximation for WTAP, but despite much progress on special cases, the factor 2 remained unbeaten for several decades.
In this talk we present two algorithms for WTAP that improve on this longstanding approximation ratio of 2. The first algorithm is a relative greedy algorithm, which starts with a simple, though weak, solution and iteratively replaces parts of this starting solution by stronger components.
This algorithm achieves an approximation ratio of (1+ln(2)+ϵ)<1.7. Second, we present a local search algorithm that achieves an approximation ratio of 1.5+ϵ (for any constant ϵ>0).
This is joint work with Rico Zenklusen.
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Host Faculty: Dr. Arindam Khan