How to Start Bellman Ford Routing Projects Using MATLAB

To start Bellman-Ford Routing Algorithm in MATLAB which is a classic algorithm that is utilised to determine the shortest route in a weighted graph, from a single source node to every other nodes including negative edge weights. Below is a step-by-step guide how to start a Bellman-Ford Routing Project using MATLAB:

Steps to Start Bellman-Ford Routing Project in MATLAB

  1. Understand Bellman-Ford Algorithm
  • Bellman-Ford functions which is iteratively reducing every edges within in the graph.
  • It is equipped to identify negative weight cycles.
  • Complexity: O(V×E)O(V \times E)O(V×E)

Here, VVV is the volume of vertices and EEE is the number of edges.

  1. Set Project Objectives

Describe the project’s goals like:

  • Replicate the routing with the help of Bellman-Ford procedure.
  • It manages the graphs including negative weights.
  • Equate the Bellman-Ford with other algorithms such as Dijkstra.
  1. Define Network Topology

It denotes the network like an adjacency matrix or an edge list.

Example: Using an Edge List

% Define the graph as an edge list

edges = [

1 2 6;  % Edge from node 1 to 2 with weight 6

1 3 5;  % Edge from node 1 to 3 with weight 5

2 3 -2; % Edge from node 2 to 3 with weight -2

2 4 5;  % Edge from node 2 to 4 with weight 5

3 5 -1; % Edge from node 3 to 5 with weight -1

4 5 2;  % Edge from node 4 to 5 with weight 2

5 4 3;  % Edge from node 5 to 4 with weight 3

];

numNodes = 5; % Total number of nodes

  1. Implement the Bellman-Ford Algorithm

This algorithm iteratively modernizes the shortest path distances for every node.

MATLAB Implementation:

function [dist, pred] = bellmanFord(edges, numNodes, src)

% Initialize distances and predecessors

dist = inf(1, numNodes);

pred = -ones(1, numNodes);

dist(src) = 0;

% Relax all edges |V|-1 times

for i = 1:numNodes-1

for j = 1:size(edges, 1)

u = edges(j, 1); % Source node

v = edges(j, 2); % Destination node

weight = edges(j, 3); % Edge weight

if dist(u) + weight < dist(v)

dist(v) = dist(u) + weight;

pred(v) = u;

end

end

end

% Check for negative weight cycles

for j = 1:size(edges, 1)

u = edges(j, 1);

v = edges(j, 2);

weight = edges(j, 3);

if dist(u) + weight < dist(v)

error(‘Graph contains a negative weight cycle.’);

end

end

end

  1. Run the Algorithm

Request the function including described edge list and source node.

% Run Bellman-Ford

srcNode = 1; % Start node

[dist, pred] = bellmanFord(edges, numNodes, srcNode);

% Display results

fprintf(‘Shortest distances from Node %d:\n’, srcNode);

disp(dist);

fprintf(‘Predecessor nodes:\n’);

disp(pred);

  1. Reconstruct Paths

Rebuild the shortest paths from the source to any destination to utilise the predecessor array.

function path = reconstructPath(pred, dest)

path = [];

current = dest;

while current ~= -1

path = [current, path];

current = pred(current);

end

end

% Example: Get the path from Node 1 to Node 5

destNode = 5;

path = reconstructPath(pred, destNode);

fprintf(‘Path from Node %d to Node %d: %s\n’, srcNode, destNode, mat2str(path));

  1. Visualize the Network

Envision the network and emphasise the shortest paths.

% Plot the graph

G = digraph(edges(:, 1), edges(:, 2), edges(:, 3));

plot(G, ‘EdgeLabel’, G.Edges.Weight);

% Highlight the path

highlightPath = reconstructPath(pred, destNode);

highlight(plot(G), highlightPath, ‘EdgeColor’, ‘r’, ‘LineWidth’, 2);

title(‘Bellman-Ford Shortest Path’);

  1. Evaluate Performance

We need to estimate and examine the performance like:

  • Path Optimality: Confirm that the paths are shortest, which is optimal route.
  • Convergence Time: Measure the performance of algorithm on large graphs.
  • Cycle Detection: Experiment with and without negative weight cycles.
  1. Extend the Project

Integrate more advanced aspects:

  • Equate the Bellman-Ford including Dijkstra’s algorithm.
  • Add real-world information like road networks or telecommunication graphs.
  • It manages the dynamic edge updates and re-execute Bellman-Ford algorithm.

Complete Example Code

% Define graph as edge list

edges = [

1 2 6;

1 3 5;

2 3 -2;

2 4 5;

3 5 -1;

4 5 2;

5 4 3;

];

numNodes = 5;

srcNode = 1;

% Run Bellman-Ford algorithm

[dist, pred] = bellmanFord(edges, numNodes, srcNode);

% Display shortest distances and paths

fprintf(‘Shortest distances from Node %d:\n’, srcNode);

disp(dist);

% Reconstruct and display path to a destination

destNode = 5;

path = reconstructPath(pred, destNode);

fprintf(‘Path from Node %d to Node %d: %s\n’, srcNode, destNode, mat2str(path));

% Visualize the graph and path

G = digraph(edges(:, 1), edges(:, 2), edges(:, 3));

plot(G, ‘EdgeLabel’, G.Edges.Weight);

highlight(plot(G), path, ‘EdgeColor’, ‘r’, ‘LineWidth’, 2);

title(‘Bellman-Ford Shortest Path’);

By following these steps, you can simulate the Bellman Ford Routing Projects, estimate the performance and visualize it using MATLAB environment. If you want more functionality or improvements, we will assist you.