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MATH-513: Metric embeddings

Summary

The course aims to introduce the basic concepts and results on metric embeddings, or more precisely on approximate embeddings. This area has been under rapid development since the 90's and it has strong impact on algorithms for discrete optimization problems.

Lectures

Instructor

Friedrich Eisenbrand

Friedrich Eisenbrand's main research interests lie in the field of discrete optimization, in particular in algorithms and complexity, integer programming, geometry of numbers, and applied optimization. He is best known for his work on efficient algorithms for integer programming in fixed dimension and the theory of cutting planes, which are an important tool to solve large scale industrial optimization problems in practice. Before joining EPFL in March 2008, Friedrich Eisenbrand was a full professor of mathematics at the University of Paderborn. Friedrich received the Heinz Maier-Leibnitz award of the German Research Foundation (DFG) in 2004 and the Otto Hahn medal of the Max Planck Society in 2001.

Official source

https://edu.epfl.ch/coursebook/en/metric-embeddings-MATH-513

Moodle Page

http://go.epfl.ch/MATH-513

About this result

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Summary

Lectures

Instructor

Friedrich Eisenbrand

Official source

https://edu.epfl.ch/coursebook/en/metric-embeddings-MATH-513

Moodle Page

http://go.epfl.ch/MATH-513

About this result

Lectures in this course (27)

Metrics: Line and Convex Cone Log in to Mediaspace to watch this video

Covers line metrics, convex cones, and linear metric combinations.

Decomposition into Line Metrics: Example and Outlook Log in to Mediaspace to watch this video

Covers the decomposition into line metrics, providing examples and discussing its implications.

Sparsest Cut and Concurrent Flow Log in to Mediaspace to watch this video

Covers sparsest cut, NP-completeness, Bougains Theorem, and concurrent flow in graphs.

Optimization of Pseudometrics in Graphs Log in to Mediaspace to watch this video

Covers the optimization of pseudometrics in graphs, focusing on minimizing pseudometrics and the shortest path metric.

Sparsest Cut: (log n) Approximation Algorithm Log in to Mediaspace to watch this video

Covers the (log n) approximation algorithm for the sparsest cut problem, presenting the mathematical theorems and proofs.

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