Dijkstra’s Algorithm: Shortest Path Routing Algorithm/ How do you solve Dijkstra’s shortest path algorithm?

Hello Friends, In this blog post, I am going to let you know about an interesting shortest path algorithm which is also known as the Dijkstra’s Algorithm.

Inside this blog post we will discuss few important questions related to Dijkstra Algorithm like

What is Dijkstra’s algorithm for example? How do you use Dijkstra’s algorithm? Does Dijkstra’s algorithm always work? Is Dijkstra a BF? Why the Dijkstra algorithm is greedy? Which shortest path algorithm is best?….

…How does the Kruskal algorithm work? Is Dijkstra greedy or dynamic programming? How do you find the shortest path algorithm? How do you solve Dijkstra’s problem? How does Prim’s algorithm work?…

…What is the time complexity of the Dijkstra algorithm? Why does Dijkstra fail negative weights? Does Google Maps use Dijkstra? What is the finiteness of the algorithm? What do you mean by shortest path algorithm?…

…What is single source shortest path algorithm? Is Bellman Ford greedy? What algorithm does GPS use?

How do you find the shortest path between two nodes?/ Dijkstra’s algorithm steps?/ What is Dijkstra’s algorithm for example?

This ‘Dijkstra algorithm’ technique is widely used in many forms because it is simple and easy to understand. The idea is to make a graph of the subnet, with each node of the graph representing a router and each arc of the graph representing a communication line(often known as a link).

For selecting a route between a given pair of routers, the algorithm just finds the shortest path between them on the graph. One method of measuring path length is the number of hops.

Using this metric, the paths ABC and ABE are equally long as shown in fig1. Another metric is the geographic distance in kilometers, in which case ABC is much longer than ABE.

Several other metrics are also possible besides hops and physical distance. As an example, each arc could be labeled with the mean queueing and transmission delay for some standard test packets determined by hourly test runs.

Dijkstra shortest path algorithmnew
Fig 1. Dijkstra’s Algorithm: Dijkstra shortest path algorithm

The shortest path is the fastest path with this graph labeling, rather than the path with the fewest arcs or kilometers. Generally, the labels on the arcs could be computed as a function of the distance, bandwidth, average traffic, communication cost, mean queue length, measured delay, and other factors.

Then the algorithm would compute the shortest path by changing the weighting function, measured according to any one of a number of criteria or a combination of criteria.

Many algorithm for computing the shortest path between two nodes of a graph are known. every node is labeled with its distance from the source node along the best-known path.

In starting, the paths are not known, therefore all nodes are labeled with infinity. As the algorithm proceeds and paths are obtained, the labels may change, reflecting better paths.

A label may be either permanent or tentative. All labels are tentative in starting. When it is discovered that a label tells the shortest possible path from the source to that node, it is made permanent and never changed thereafter.

For illustrating the working of labeling algorithm see at the weighted undirected graph of fig1(a) where the weights represent distance. For finding the shortest path from A to D.

We start out by marking node A as permanent, denoted by a filled-in circle. Then, each of the nodes adjacent to A (the working node), relabeling each one with the distance to A.

Whenever a node is relabeled, it is also labeled with the node from which the probe was made, therefore the final path can be constructed later. After examining each of the nodes adjacent to A,…

all the tentatively labeled nodes are examined in the whole graph and made the one with the smallest label permanent as shown in fig1(b). This one is the new working node.

Now, starting is done from B and all nodes adjacent to it are examined. If the sum of the label on B and the distance from B to the node being considered is less than the label on that node, a shorter path is obtained, therefore the label is relabeled.

When all the nodes adjacent to the working node have been inspected and the tentative labels changed if possible, the whole graph is searched for the tentatively labeled node with the smallest value.

This node is made permanent and is the working node for the next round. The first five steps of the algorithm are shown in fig1.

Quick Q&A:

How do you use Dijkstra’s algorithm?

There are few simple steps of Dijkstra algorithm which is given below to find the shortest distance.

Very first you need to initialize the distance as per the Dijkstra algorithm.
After initializing the node pick the first node and calculate the distance to the adjacent nodes.
Here pick the shortest distance node out of all the adjacent nodes.
Now again repeat the process and calculate all the adjacent nodes calculation with the new node which we have found in the previous search.
And doing this you will find the shortest path or tree between two vertex or nodes in the graph using Dijkstra Algorithm.

Does Dijkstra’s algorithm always work?

Dijkstra algorithm works correctly for all the weighted and directed graph with non-negative weights and easily able to find the shortest path between two given vertex.

Is Dijkstra a BF?

We can say that the Dijkstra algorithm does the same as BFS does. Dijkstra algorithm relies on the property of shortest path as s to t and also between any pair of vertices along the path. So we can conclude that the Dijkstra algorithm can be implemented as the BFS with the priority queue however it is not the only implementation.

Why the Dijkstra algorithm is greedy?


There are both scenarios with the Dijkstra algorithm. It can be considered as greedy as we choose the closest vertex. And on the other end, it can be also considered as dynamic as we update the value with the help of previously calculated values. But we would like to consider it closer to the dynamic algorithm than the greedy algorithm. As we can’t predict the step by step process to calculate the shortest distance between A to B.

Which shortest path algorithm is best?

With the Dijkstra Algorithm’s help, we are able to find the shortest path from one vertex whereas the Floyd-Warshall algorithm is able to find out the shortest distance between each pair of vertices as it is a higher running time than the Dijkstra algorithm.

How does the Kruskal algorithm work?

Kruskal algorithm is used to find the minimum spanning tree from an undirected connected weighted graph. In each step, we have to find out the lowest weight node that should not form a cycle in the spanning tree.

How do you find the shortest path algorithm? What are the algorithms for finding the shortest path?

For finding the shortest path Dijkstra algorithm is not only the single option rather you can find it with the help of some other shortest path algorithm which is given below:

BFS(Breath-first-search)
DFS(Depth-first-search)
Bidirectional search
Dijkstra Algorithm
Bell-Man Ford algorithm

How does Prim’s algorithm work?

Prim’s algorithm is also known as Jarnik’s algorithm and it is a greedy algorithm that is used to find the minimum spanning tree without forming any cycle out of an undirected connected and weighted graph.

What is the time complexity of the Dijkstra algorithm?

O(V 2) is the time complexity of the Dijkstra algorithm. But when it is the case of the min-priority queue it is down to O(V + E log V).

Why does Dijkstra fail negative weights?

The main aim of the Dijkstra algorithm is to find the optimal path instead of just finding any path. So with the negative weights, it can not find the optimal path as it can not form any loop with the nodes that it has visited before. So with the negative weights, it will end to any random path but not the perfect optimal path.

Does Google Maps use Dijkstra?

This is the fact that the Dijkstra algorithm power the shortest pathfinding in an effective way. And we can say that all navigation applications like Google Map, Apple Map are using Dijkstra algorithm or another search algorithm may be a little extended and updated form but surely include the basics of these search algorithm like Dijkstra algorithm.

Can Dijkstra find the longest path?

The basic use of the Dijkstra algorithm is to find the shortest route from one starting vertex say ‘i’ to an end vertex say j. But Dijkstra algorithm can also be used to find the longest distance or route if some simple modification update is made.

What is the difference between Bellman-Ford and Dijkstra?

Both are used to find the optimal path or shortest path between two pair of vertices but the only main difference between them is that Bellman is capable to handle the negative weights within the edges and Dijkstra algorithm is not capable to handle the negative weights, it can only work perfectly with the positive weights.

What is the difference between BFS and Dijkstra’s algorithms?

Both are quite similar but have some minor differences. BFS is used to calculate the shortest distance or path in an undirected graph whereas in the Dijkstra algorithm we find the shortest path in the directed graph.

Conclusion:

So, in this blog post we have learned about the Dijkstra algorithm and other few search algorithms for finding the shortest path or optimal path. We have also seen the process step by step to solve the shortest path problem using Dijkstra algorithm.

Within this blog post, we have gone through What is Dijkstra’s algorithm with an example, How do you use Dijkstra’s algorithm, Does Dijkstra’s algorithm always work, Is Dijkstra a BF, Why Dijkstra algorithm is greedy, Which shortest path algorithm is best, How does Kruskal algorithm work, Is Dijkstra greedy or dynamic programming, How do you find shortest path algorithm, How do you solve Dijkstra’s problem, How does Prim’s algorithm work, What is the time complexity of Dijkstra algorithm, Why does Dijkstra fail negative weights, Does Google Maps use Dijkstra, What is the finiteness in an algorithm, What do you mean by shortest path algorithm, What is single-source shortest path algorithm, Is Bellman-Ford greedy, What algorithm does GPS use.

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Anurag

I am a blogger by passion, a software engineer by profession, a singer by consideration and rest of things that I do is for my destination.