Lecture

Conditional Statements & Graph Theory

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

CS-451: Distributed algorithms

Computing is nowadays distributed over several machines, in a local IP-like network, a cloud or a P2P network. Failures are common and computations need to proceed despite partial failures of machines or communication links. This course will study the fo ...

Description

This lecture covers conditional statements, including the converse, contrapositive, and inverse, as well as exercises related to proof by cases and contradiction. It then delves into graph theory, discussing graphs, paths, connectivity, and k-connectivity. The lecture also explores gossip protocols, robustness to failures, random failures, and Erdös-Renyi graphs, highlighting their connectivity properties and applications in distributed systems.

Instructor

Rachid Guerraoui

Rachid Guerraoui has been affiliated with Ecole des Mines of Paris, the Commissariat à l'Energie Atomique of Saclay, Hewlett Packard Laboratories and the Massachusetts Institute of Technology. He has worked in a variety of aspects of distributed computing, including distributed algorithms and distributed programming languages. He is most well known for his work on (e-)Transactions, epidemic information dissemination and indulgent algorithms. He co-authored a book on Transactional Systems (Hermes) and a book on reliable distributed programming (Springer). He was appointed program chair of ECOOP 1999, ACM Middleware 2001, IEEE SRDS 2002, DISC 2004 and ACM PODC 2010. His publications are available at http://lpdwww.epfl.ch/rachid/papers/generalPublis.html

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (29)

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.

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.

Graph (discrete mathematics)

In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.

Degree (graph theory)

In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. The degree of a vertex is denoted or . The maximum degree of a graph , denoted by , and the minimum degree of a graph, denoted by , are the maximum and minimum of its vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0.

Related lectures (64)

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Belief Propagation

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Connectivity in Graph Theory

Covers the fundamentals of connectivity in graph theory, including paths, cycles, and spanning trees.

Cheeger's Inequalities

Explores Cheeger's inequalities for random walks on graphs and their implications.