Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 12, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Goran Zuzic

Low-Congestion Shortcuts are Universally Optimal for Distributed Computing

The modern computation and information processing systems shaping our world have become massively distributed and a fundamental understanding of distributed algorithmics has never been more important. At the same time, despite 40 years of intense study, we do not have a satisfactory understanding of how a network topology influences the runtime of various distributed tasks.

I will present a new result that resolves the question in many interesting ways. Concretely, suppose we are solving a distributed optimization problem (e.g., minimum spanning tree problem, minimum cut, or shortest path) in the classic CONGEST model of distributed computing. The work shows, via an information-theoretic argument, that a fast distributed algorithm for any of the above problems induces a specific combinatorial structure in the graph called "low-congestion shortcuts". In other words, the non-existence of this structure represents the first non-trivial lower bound on the runtime of distributed optimization tasks that can be applied to any network topology. Moverover, the lower bound holds even when all the nodes know the entire network topology in advance.

Furthermore, in other work, we show that the bound is tight in the known-topology setting---the existence of low-congestion shortcuts implies the existence of fast distributed algorithms for the above problems. Together, these two results resolve a long-standing open problem posed in [Garay, Kutten, Peleg; 1998] about identifying the salient network topology parameters that characterize the runtime of various problems in distributed optimization, at least in the known-topology setting.

This talk presents joint work with Bernhard Haeupler and David Wajc.

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