## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, June 08, 2017, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Jason Li (Carnegie Mellon University)

## Shortcuts in Excluded Minor Graphs

Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This talk presents a fast distributed algorithm for such problems in the CONGEST model, for graph networks which exclude a fixed minor.

On general graphs, many optimization problems, including the ones mentioned above, require $\tilde\Omega(\sqrt n)$ rounds of communication in the CONGEST model, even if the network graph has much smaller diameter. Naturally, the next step in algorithm design is to design efficient algorithms which bypass this lower bound on a restricted class of graphs. Currently, the only known method of doing so uses the low-congestion shortcut framework of Ghaffari and Haeupler [SODA'16]. Building off of their work, this paper proves that excluded minor graphs admit high-quality shortcuts, leading to an $\tilde O(D^2)$ round algorithm for the aforementioned problems.

Even though the proof is deeply involved, merely showing the existence of good shortcuts is sufficient to obtain simple, efficient distributed algorithms. In particular, the shortcut framework can efficiently construct near-optimal shortcuts and then use them to solve the optimization problems.

Based on a joint work with ​ Bernhard Haeupler and Goran Zuzic.

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