Abstract
Many modern systems are built on top of large-scale networks like the Internet. This article provides an overview of a dissertation [29] that addresses the complexity of classic graph problems like the vertex coloring problem in such networks. It has been known for a long time that randomization helps significantly in solving many of these problems, whereas the best known deterministic algorithms have been exponentially slower. In the first part of the dissertation we use a complexity theoretic approach to show that several problems are complete in the following sense: An efficient deterministic algorithm for any complete problem would imply an efficient algorithm for all problems that can be solved efficiently with a randomized algorithm. Among the complete problems is a rudimentary looking graph coloring problem that can be solved by a randomized algorithm without any communication. In further parts of the dissertation we develop efficient distributed algorithms for several problems where the most important problems are distributed versions of integer linear programs, the vertex coloring problem and the edge coloring problem. We also prove a lower bound on the runtime of any deterministic algorithm that solves the vertex coloring problem in a weak variant of the standard model of the area.
Article note
The dissertation of Dr. Yannic Maus has received the GI Dissertation Award 2018 and the 2019 Wolfgang-Gentner Award for the Promotion of Young Scientists.
About the author
Dr. Yannic Maus studied Mathematics and Computer Science at the RWTH Aachen University and the National University of Singapore where he received the Springorum-Denkmünze RWTH Aachen University Award for his studies. After his master studies he pursued a PhD from the Albert-Ludwigs-Universität Freiburg under the supervision of Professor Dr. Fabian Kuhn and in October 2018 he graduated summa cum laude in the area of distributed graph algorithms. For his dissertation he received the dissertation award of the German Informatics Society 2018 and the 2019 Wolfgang-Gentner Award for the Promotion of Young Scientists. Afterwards he moved to the country with the largest density of excellent researchers in the area of distributed algorithms, that is, he moved to the Technion (
) in Haifa, Israel , where he works as a postdoctoral researcher in the group of Professor Dr. Keren Censor-Hillel. In his leisure time he loves riding his (road) bike or the joys of cross country skiing.
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