Lecture

Bellman Ford: Shortest Paths

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-250: Algorithms I

The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing algorithms, elementary data structures, major algorithmic paradigms such as dynamic programming, s ...

Description

This lecture covers the Bellman-Ford algorithm for finding shortest paths in a directed graph with edge weights. It explains problem variants like single-source, single-destination, single-pair, and all-pairs shortest paths. The algorithm iteratively updates shortest-path estimates and detects negative cycles. Runtime analysis and implementation details are discussed, along with an example and final comments on its applications in routing and dynamic networks.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (3)

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.

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

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (32)

Directed acyclic graph

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions.

Cycle graph

In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with n vertices is called C_n. The number of vertices in C_n equals the number of edges, and every vertex has degree 2; that is, every vertex has exactly two edges incident with it. There are many synonyms for "cycle graph".

Dynamic routing

Dynamic routing, also called adaptive routing, is a process where a router can forward data via a different route for a given destination based on the current conditions of the communication circuits within a system. The term is most commonly associated with data networking to describe the capability of a network to 'route around' damage, such as loss of a node or a connection between nodes, as long as other path choices are available. Dynamic routing allows as many routes as possible to remain valid in response to the change.

Cycle (graph theory)

In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal. A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree. A circuit is a non-empty trail in which the first and last vertices are equal (closed trail).

Line graph

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this.

Related lectures (64)

Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Shortest Paths: Negative Weights & Applications

Covers Minimum Spanning Trees, Kruskal's Algorithm, and Shortest Paths in directed graphs.

Bellman-Ford Algorithm: Shortest Path Estimation

Explains the Bellman-Ford algorithm for finding the shortest path in a directed graph with edge weights.

Shortest Path in Directed Graphs

Covers finding the shortest path in directed graphs efficiently using algorithmic approaches and discussing related NP-complete problems.

Causal Inference & Directed Graphs