The course will cover some traditional discrete approaches to various graph problems, especially flow problems, and then contrast these approaches with modern, asymptotically faster methods based on combining convex optimization with spectral and combinatorial graph theory.

The contents of this summary are based on the lecture “Advanced Graph Algorithms and Optimization” given by Rasmus Kyng at ETH Zurich in the spring of 2022. Certain parts are similar/taken from the lec-ture notes. network of resistors. Such a network G = (V, E, r) can be de-scribed by a set of vertices V, set of wires (or edges) E, and resis-

This course will cover a number of advanced topics in optimization and graph algorithms. graph algorithms using convex optimization techniques. phenomena in optimization. optimization with spectral and combinatorial graph theory. acceleration, preconditioning, and non-Euclidean optimization. spectral and combinatorial preconditioning.

In addition, it presents three efficient and scalable advanced graph algorithms – the subgraph enumeration, cohesive subgraph detection, and graph extraction algorithms.

The goals of this practical course are as follows: Improve on your teamwork, improve your programming skills, learn new and advanced graph algorithms, and familiarize yourself with contributing to active open source projects And hopefully: Extend existing graph libraries with new algorithms. Today you will form two teams.

Course description: Fast algorithms for fundamental graph optimization problems, including maximum flow, minimum cuts, minimum spanning trees, nonbipartite matching, planar separators and applications, and shortest paths. Data structures including Fibonacci heaps, …

These notes are based on material from “Advanced Graph Algorithms and Optimization” taught by Rasmus Kyng at ETH Zurich in the summer of 2022. Notes. Contents are convex optimization, spectral graph theory, and combinatorial graph algorithms. …

Understanding how to traverse, search, and optimize graphs is essential, particularly when it involves finding the shortest path between nodes, mapping routes, or determining any associations between specific data points.

An image can be seen as a structured graph, where pixels of the image are associated to nodes. A node is classically linked by edges to its four nearest neighbors, corresponding to its four “nearest” pixels in the cardinal directions. A variety of more complex graphs exists and

Course Objective: The course will take students on a deep dive into modern approaches to graph algorithms using convex optimization techniques. By studying convex optimization through the lens of graph algorithms, students should develop a deeper understanding of fundamental phenomena in optimization.