Distribute the different diagrams to different pairs of students around the room. How much time does it take to run?
Was the shortest path always the same? You and your partner will be given the algorithm and a graph. Which of the following statements is FALSE about minimum spanning trees from the previous lesson and shortest path trees: Typically one student will read the instructions while the other keeps track of information on the graph diagram.
Give individual students time to work on finding the shortest paths for the small examples in the worksheet. If not, why not?
The reason we have routers is because we want to send messages from our router to lots and lots of different locations. In the shortest path problem, we have to do some processing of every node and every edge. Is there anyway to stop early?
As an easy example to think about: There are different 8 diagrams; each is the same graph but with a different source node indicated. Some algorithms on graphs require you to process nodes and edges multiple times.
This is a potential factor when thinking about time. And together you will act as the computer, interpreting the instructions and trying to trace out the algorithm and follow its steps. Then pair students to compare their answers. Students should work in pairs to step through the algorithm and trace it out.
What about the path between the two source nodes? Teaching Guide Getting Started Introductory remarks: Compare the shortest path diagrams; these form a tree extending from the source node.
So the shortest path problem is dependent on the total number of nodes and edges in the graph. When running the algorithm, it is possible that the very last edge might cause a path to change. Based on your experience, would this algorithm find the shortest path for any graph of nodes and edges?
It has the same theoretical running time in the worst case as SSSP. Will it always solve the problem with a correct solution? However, you should still have students try their hand at the set of problems on the second page. The worksheet asks students to find the shortest path between two nodes on a series of graphs.
Time is an interesting element when talking about computer algorithms. The most important things are those that get performed repeatedly as part of the algorithm. For Shortest Path you can only stop after you have processed every edge.
So with MST, it was dependent on the number of nodes and edges, but we could stop after we found n-1 edges. Can you guarantee that you could always stop early?
Worksheet - Intro to the Shortest Path Problem. Once students finish, put pairs together to make groups of 4.Dijkstra's algorithm, named after its discoverer, Dutch computer scientist Edsger Dijkstra, is a greedy algorithm that solves the single-source shortest path problem for a directed graph with non negative edge weights.
Given a graph and a source vertex in graph, find shortest paths from source to all vertices in the given graph. We have discussed Dijkstra’s Shortest Path algorithm in.
I am working through a shortest path problem using Dijkstra's Algorithm. I am having trouble because the algorithm is supposed to provide the shortest path, but after running the algorithm I get a Dijkstra's Algorithm Does not generate Shortest Path?
Ask Question. up vote 2 down vote favorite. 2. You are implementing the Greedy. Apr 09, · In this video I show how a greedy algorithm can and cannot be the optimal solution for a shortest path mapping problem. As with the majority of algorithm problems, it is key to understand the data that you will be dealing with, or else you could end up with a very poor performing solution.
Like Prim’s MST, we generate a SPT (shortest path tree) with given source as root. We maintain two sets, one set contains vertices included in shortest path tree, other set includes vertices not yet included in shortest path tree.
Dijkstra algorithm is also called single source shortest path algorithm. It is based on greedy technique. The algorithm maintains a list visited[ ] of vertices, whose shortest distance from the source is already known.Download