How to Start Dijkstra’s Link State Projects Using MATLAB

To start a Dijkstra’s Link State Routing project using MATLAB, we will want to replicate a network in which every single node understands the entire network topology that is the full graph and determines the shortest route individually to all other nodes to utilise Dijkstra’s algorithm within the network. Dijkstra’s algorithm is a familiar shortest-path algorithm which is utilised for computing the best path within a weighted graph from a source node to every other node in which the edge weights denote the cost or distance among the nodes.

Periodically each node transmits data regarding their immediate neighbors (link states) to all other nodes within Link State Routing. According to this, every single node could determine the shortest path individually to every other node within the network to utilise Dijkstra’s algorithm. Below is a sequential method to get started:

Steps to Start Dijkstra’s Link State Routing in MATLAB

  1. Network Representation

Initially, we create the network topology. In a link-state routing model, we will denote the network like a graph, where:

  • Nodes signify routers or network devices.
  • Edges denote the direct interaction links among the nodes.
  • Weights on edges signify the link costs such as distance, delay, and bandwidth.

We need to utilise an adjacency matrix or graph object for signifying the network in MATLAB.

Example:

% Define the adjacency matrix for a simple network (5 nodes)

adjMatrix = [

0, 10, inf, 30, inf;  % Node 1: Connected to node 2 (cost 10) and node 4 (cost 30)

10, 0, 50, inf, inf;  % Node 2: Connected to node 1 (cost 10) and node 3 (cost 50)

inf, 50, 0, 10, 60;   % Node 3: Connected to node 2 (cost 50), node 4 (cost 10) and node 5 (cost 60)

30, inf, 10, 0, 20;   % Node 4: Connected to node 1 (cost 30), node 3 (cost 10) and node 5 (cost 20)

inf, inf, 60, 20, 0    % Node 5: Connected to node 3 (cost 60) and node 4 (cost 20)

];

% Use an adjacency matrix where ‘inf’ represents no direct connection

% Create the graph object for visualization

G = graph(adjMatrix);

plot(G, ‘Layout’, ‘force’);

title(‘Network Topology’);

  1. Dijkstra’s Algorithm Implementation

Dijkstra’s algorithm helps to determine the shortest path in the graph from a source node to all other nodes. The main steps contain:

  1. Configure the distance to the source node to 0 and the distances to every other node to eternity.
  2. Specify every node like unvisited.
  3. Compute the tentative distance via present node for each unvisited node.
  4. Denote the present node like visited and repeat this process until every node has been visited.

Below is a MATLAB execution of Dijkstra’s Algorithm to utilise adjacency matrix:

Dijkstra’s Algorithm Function:

function [shortestDist, path] = dijkstra(adjMatrix, source)

n = size(adjMatrix, 1);   % Number of nodes

shortestDist = inf(1, n);  % Distance from source to each node

shortestDist(source) = 0;  % Distance to source is 0

visited = false(1, n);     % Keep track of visited nodes

previous = NaN(1, n);      % To store the previous node in the shortest path

while true

% Find the unvisited node with the smallest tentative distance

[~, currentNode] = min(shortestDist .* ~visited + inf(1, n) .* visited);

% If all nodes are visited or remaining distances are infinite, break

if shortestDist(currentNode) == inf

break;

end

% Mark the current node as visited

visited(currentNode) = true;

% Update distances to neighboring nodes

for neighbor = 1:n

if adjMatrix(currentNode, neighbor) ~= inf && ~visited(neighbor)

% Calculate tentative distance to the neighbor node

newDist = shortestDist(currentNode) + adjMatrix(currentNode, neighbor);

if newDist < shortestDist(neighbor)

shortestDist(neighbor) = newDist;

previous(neighbor) = currentNode;

end

end

end

end

% Reconstruct the shortest path

path = [];

currentNode = n;  % You can change this to the destination node index

while ~isnan(previous(currentNode))

path = [currentNode, path];

currentNode = previous(currentNode);

end

path = [source, path];  % Add source node at the beginning

end

  1. Using the Dijkstra Function

Next, we can utilise the dijkstra function for determining the shortest path from a source node to all other nodes.

Example:

sourceNode = 1;  % Node 1 is the source

[distances, path] = dijkstra(adjMatrix, sourceNode);

disp(‘Shortest Distances from Source Node:’);

disp(distances);

disp(‘Shortest Path to Destination Node (Node 5):’);

disp(path);

This function will be executed to find shortest distance from the source node to all other nodes and then it will return the shortest path to a destination (e.g., from node 1 to node 5).

  1. Link State Advertisement and Network Topology

Each node transmits their link state to all other nodes within the network in a Link State Routing protocol. Then, every single node utilises this data to form an entire network map and compute the shortest route.

In MATLAB, to simulate this, we can:

  • Mimic the method in which each node transmits their link state to other nodes periodically.
  • Each node according to the link states it obtains and builds the network graph (adjacency matrix) and then calculates the shortest paths.

For instance, when each node calculates their shortest path with the support of Dijkstra’s algorithm then it can swap this data including their neighbors and modernizing its routing table.

  1. Simulating Link State Updates

We can modernize the adjacency matrix periodically and re-execute the Dijkstra algorithm for replicating periodic updates of link states (for example, once the network topology modifies or when nodes update its link costs).

Example:

% Simulate network changes (e.g., a new link is added between Node 2 and Node 4)

adjMatrix(2, 4) = 20;  % Add a new link between Node 2 and Node 4 with cost 20

adjMatrix(4, 2) = 20;  % Make the link bidirectional

% Re-run Dijkstra’s algorithm after the change

[distances, path] = dijkstra(adjMatrix, sourceNode);

disp(‘Updated Shortest Distances from Source Node:’);

disp(distances);

disp(‘Updated Shortest Path to Destination Node (Node 5):’);

disp(path);

  1. Visualizing the Network and Routing Path

We can be utilised MATLAB’s built-in graph plotting functions for envisioning the network and the shortest path.

Example:

% Plot the network

G = graph(adjMatrix);

figure;

plot(G, ‘Layout’, ‘force’);

title(‘Network Topology’);

% Visualize the shortest path from the source node to the destination node

hold on;

pathNodes = path;  % Extract the nodes along the shortest path

for i = 1:length(pathNodes)-1

plot([G.Nodes.X(pathNodes(i)), G.Nodes.X(pathNodes(i+1))], …

[G.Nodes.Y(pathNodes(i)), G.Nodes.Y(pathNodes(i+1))], ‘r-‘, ‘LineWidth’, 2);

end

hold off;

This will envision the network and emphasize the shortest path among the source and destination nodes within red color.

  1. Extending the Project

When we contain simple Dijkstra’s Link State Routing execution then we need to prolong the project including numerous aspects:

  • Link State Advertisement (LSA) Simulation: In the network, design how nodes broadcast its link state periodically to all other nodes.
  • Dynamic Network Topology: Replicate the modifications within the network like link failures or node mobility, and consequently modernize the network graph and shortest paths.
  • Performance Analysis: Examine the Dijkstra’s algorithm performance such as computation time, memory usage, and scalability for large networks.
  • Routing Tables: According to the computed shortest paths, sustain and bring up-to-date routing tables at each node.

You can begin simulating and analysing the Dijkstra’s Link State project using OMNeT++ environment by following these steps and expand it to examine multiple functionalities.