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# Dijkstra’s Algorithm PowerPoint PPT Presentation

Dijkstra’s Algorithm. Terminology. Graph (G) : A set of items connected by edges. Each item in a graph is called a vertex or edge. Vertex (V) : An item in a graph, sometimes referred to as a node. (A node is a unit of reference in a data structure.)

Dijkstra’s Algorithm

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### Terminology

• Graph (G) : A set of items connected by edges. Each item in a graph is called a vertex or edge.

• Vertex (V) : An item in a graph, sometimes referred to as a node. (A node is a unit of reference in a data structure.)

• Edge (E) : A connection between two vertices of a graph.

• Weighted Graph : A graph which has a weight, or number, associated with each edge.

### Dijkstra’s Algorithm is…

• Named after it’s creator E.W. Dijkstra. He is a Professor of Mathematic at the University of Amsterdam.

• An algorithm for finding the shortest path between two vertices (or nodes). This algorithm has the added benefit of finding the shortest path from a given source to all points in the graph at the same time. Because of this it is sometimes referred to as the single-source shortest path algorithm

• Requires all edged weights to be positive.

• Its time efficiency is O (E log V).

GRAPH

Step 1 Dijkstra’s Algorithm

A can see B and C

B WINS WITH A COST OF 30!

Step 2 Dijkstra’s Algorithm

B can see C and D

C WINS WITH A COST OF 40!

Step 3 Dijkstra’s Algorithm

C can see D and E

E WINS WITH A COST OF 50!

Step 4 Dijkstra’s Algorithm

E sees nothing… However, other nodes are seen from previously seen vertices.

Completed Dijkstra’s Algorithm

Generates the following Arrays:

Dijkstra’s Algorithm is GREEDY!

• A Greedy Algorithm is defined as follows:

• An algorithm that always takes the best immediate or local, solution while finding an answer. Greedy algorithms find the overall or globally optimal solution.

Warshall’s Algorithm

O (V3)

Floyd’s Algorithm

O (V3)

Dijkstra’s Algorithm

O (E Log V)

Dijkstra WINS!!!

Group D Presentation

1)Warshall’s Algorithm

2)Floyd’s Algorithm

3)Dijkstra’s Algorithm

Prepared by:

Michael Cicarella Gabriela Ruz Marius Janusaitis