Lecture

Cheeger's Inequalities

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In course

CS-450: Algorithms II

A first graduate course in algorithms, this course assumes minimal background, but moves rapidly. The objective is to learn the main techniques of algorithm analysis and design, while building a repertory of basic algorithmic solutions to problems in many ...

Description

This lecture covers Cheeger's inequalities, focusing on random walks in graphs, spectral partitioning, and the combinatorial properties of graphs. The instructor explains the concept of conductance, eigenvectors, and the relationship between vertices in a graph.

Instructors (3)

Mikhail Kapralov

Teaching & PhD PhD Students Weronika Wrzos-Kaminska, Guy Weissenberg, Davide Mazzali, Ekaterina Kochetkova, Kshiteej Jitesh Sheth Past EPFL PhD Students Amir Zandieh, Aidasadat Mousavifar, Navid Nouri, Jakab Tardos, Grzegorz Adam Gluch, Makarov Mikhail Past EPFL PhD Students as codirector Paritosh Garg Courses Algorithms II CS-450 The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing alg

Ola Nils Anders Svensson

Alessandro Chiesa

Alessandro Chiesa is a faculty member in computer science. He conducts research in complexity theory, cryptography, and security, with a focus on the theoretical foundations and practical implementations of cryptographic proofs that are short and easy to verify. He is a co-author of several zkSNARK libraries, and is a co-inventor of the Zerocash protocol. He has co-founded Zcash and StarkWare Industries. He is a recipient of a Sloan Research Fellowship (2021), an Okawa Foundation Research Grant (2020), and Google Faculty Research Awards (2018 and 2017). He was included in MIT Technology Review's "35 Innovators Under 35" list in 2018.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (32)

Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.

Glossary of graph theory

This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges.

Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v.

Path (graph theory)

In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A directed path (sometimes called dipath) in a directed graph is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction. Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts.

Vertex (graph theory)

In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another.

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