Course

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

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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)

Sparsest Subgraph: Densest Subgraph

Covers Sparsest Subgraph and Densest Subgraph, focusing on correlation clustering and approximation algorithms.

Rounding the relaxation: Max Sum Diversification

Explores rounding the relaxation and Max Sum Diversification, discussing effects, integral solutions, and loss bounds.

Low Diameter Random Partitioning

Discusses Low Diameter Randomized Decomposition and graph partitioning for edge cuts and coloring.

Metric Spaces and Isometric Embeddings

Covers metric spaces, isometric embeddings, and equilateral spaces with examples and proofs.

Metrics: Line and Convex Cone

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

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