Dijkstra's algorithm is a solution to the single-source shortest path problem in graph theory. It finds the shortest paths from a source vertex to all other vertices in a weighted graph where all edge weights are non-negative. The algorithm uses a greedy approach, maintaining a set of vertices whose final shortest path from the source vertex has already been determined.
This presentation gives a conceptual idea of a graphical algorithm that is Dijkstra's Algorithm. Includes general introduction , the pseudocode, code in form of QR Card, graphical. Also discussing the algorithm in form of graphical images and nodes. Also it include the complexity and application of algorithm in various ranges of fields. This is a fun, eye-catching, conceptual presentation, best suited for students into engineering.
Dijkstra's algorithm was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. He received the Turing award in 1972. The Dijkstra prize is named after him which is given for outstanding papers on the principles of distributed computing. One of his famous quote is that Computer Science is no more about computers than astronomy is about telescopes.
Dijkstra's algorithm solves the shortest-path problem for any weighted graph with non-negative weights and finds shortest distance between 2 vertices. The algorithm creates the tree of the shortest paths from the starting source vertex from all other points in the graph. Works on both directed and undirected graph. It differs from the minimum spanning tree as the shortest distance between two vertices may not be included in all the vertices of the graph.
This presentation gives a conceptual idea of a graphical algorithm that is Dijkstra's Algorithm. Includes general introduction , the pseudocode, code in form of QR Card, graphical. Also discussing the algorithm in form of graphical images and nodes. Also it include the complexity and application of algorithm in various ranges of fields. This is a fun, eye-catching, conceptual presentation, best suited for students into engineering.
Dijkstra's algorithm was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. He received the Turing award in 1972. The Dijkstra prize is named after him which is given for outstanding papers on the principles of distributed computing. One of his famous quote is that Computer Science is no more about computers than astronomy is about telescopes.
Dijkstra's algorithm solves the shortest-path problem for any weighted graph with non-negative weights and finds shortest distance between 2 vertices. The algorithm creates the tree of the shortest paths from the starting source vertex from all other points in the graph. Works on both directed and undirected graph. It differs from the minimum spanning tree as the shortest distance between two vertices may not be included in all the vertices of the graph.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
The solution to the single-source shortest-path tree problem in graph theory. This slide was prepared for Design and Analysis of Algorithm Lab for B.Tech CSE 2nd Year 4th Semester.
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.
It is related to Analysis and Design Of Algorithms Subject.Basically it describe basic of topological sorting, it's algorithm and step by step process to solve the example of topological sort.
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
The solution to the single-source shortest-path tree problem in graph theory. This slide was prepared for Design and Analysis of Algorithm Lab for B.Tech CSE 2nd Year 4th Semester.
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.
It is related to Analysis and Design Of Algorithms Subject.Basically it describe basic of topological sorting, it's algorithm and step by step process to solve the example of topological sort.
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized
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Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
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2. Single-Source Shortest Path Problem
Single-Source Shortest Path Problem - The problem of finding shortest
paths from a source vertex v to all other vertices in the graph.
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3. Dijkstra's algorithm
Dijkstra's algorithm - is a solution to the single-source
shortest path problem in graph theory.
Works on both directed and undirected graphs. However,
all edges must have nonnegative weights.
Approach: Greedy
Input: Weighted graph G={E,V} and source vertex v∈V,
such that all edge weights are nonnegative
Output: Lengths of shortest paths (or the shortest paths
themselves) from a given source vertex v∈V to all other
vertices
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