**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Prim's algorithm

Summary

In computer science, Prim's algorithm (also known as Jarník's algorithm) is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. The algorithm operates by building this tree one vertex at a time, from an arbitrary starting vertex, at each step adding the cheapest possible connection from the tree to another vertex.
The algorithm was developed in 1930 by Czech mathematician Vojtěch Jarník and later rediscovered and republished by computer scientists Robert C. Prim in 1957 and Edsger W. Dijkstra in 1959. Therefore, it is also sometimes called the Jarník's algorithm, Prim–Jarník algorithm, Prim–Dijkstra algorithm
or the DJP algorithm.
Other well-known algorithms for this problem include Kruskal's algorithm and Borůvka's algorithm. These algorithms find the minimum spanning forest in a possibly disconnected graph; in contrast, the most basic form of Prim's algorithm only finds minimum spanning trees in connected graphs. However, running Prim's algorithm separately for each connected component of the graph, it can also be used to find the minimum spanning forest. In terms of their asymptotic time complexity, these three algorithms are equally fast for sparse graphs, but slower than other more sophisticated algorithms.
However, for graphs that are sufficiently dense, Prim's algorithm can be made to run in linear time, meeting or improving the time bounds for other algorithms.
The algorithm may informally be described as performing the following steps:
In more detail, it may be implemented following the pseudocode below.
As described above, the starting vertex for the algorithm will be chosen arbitrarily, because the first iteration of the main loop of the algorithm will have a set of vertices in Q that all have equal weights, and the algorithm will automatically start a new tree in F when it completes a spanning tree of each connected component of the input graph.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (2)

Related concepts (13)

Related lectures (400)

Related MOOCs (11)

Related courses (47)

Kruskal's algorithm

Kruskal's algorithm (also known as Kruskal's method) finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. (A minimum spanning tree of a connected graph is a subset of the edges that forms a tree that includes every vertex, where the sum of the weights of all the edges in the tree is minimized. For a disconnected graph, a minimum spanning forest is composed of a minimum spanning tree for each connected component.

Greedy algorithm

A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city.

Minimum spanning tree

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components.

Continues the discussion on Simon's hidden subgroup problem, focusing on finding a basis.

Introduces algorithms, covering their formalization, basic components, control structures, and the challenge of ensuring correctness.

Covers the Hidden Subgroup Algorithm in quantum computing, emphasizing projectors and measurement postulates.

Information, Calcul, Communication: Introduction à la pensée informatique

Dans une première partie, nous étudierons d’abord comment résoudre de manière très concrète un problème au moyen d’un algorithme, ce qui nous amènera dans un second temps à une des grandes questions d

Information, Calcul, Communication: Introduction à la pensée informatique

Dans une première partie, nous étudierons d’abord comment résoudre de manière très concrète un problème au moyen d’un algorithme, ce qui nous amènera dans un second temps à une des grandes questions d

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

The hardware complexity of modern machines makes the design of adequate programming models crucial for jointly ensuring performance, portability, and productivity in high-performance computing (HPC).

CS-119(c): Information, Computation, Communication

L'objectif de ce cours est d'introduire les étudiants à la pensée algorithmique, de les familiariser avec les fondamentaux de l'Informatique et de développer une première compétence en programmation (

CS-101: Advanced information, computation, communication I

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a

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 machin

Summary: ExpressionView is an R package that provides an interactive graphical environment to explore transcription modules identified in gene expression data. A sophisticated ordering algorithm is us

2010