Route Optimization with Dijkstra’s Algorithm

Overview

This project combines a technical description and an instructional set to explain and apply route optimization in modern navigation systems.

It first explains how road networks are modeled as weighted graphs and how Dijkstra’s Algorithm computes the shortest path. It then provides a step-by-step, usability-centered guide that allows a user to manually perform the same process.

The goal is to move from understanding → execution.

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Part 1 — Technical Description

Key Concepts

Weighted Graphs

• Nodes → intersections or endpoints
• Edges → roads connecting nodes
• Weights → travel cost (time, distance, traffic)

Dijkstra’s Algorithm

The algorithm finds the shortest path from a starting node to all other nodes by:

1. Initializing distances (start = 0, others = ∞)
2. Selecting the smallest unvisited node
3. Updating neighboring nodes (relaxation)
4. Repeating until the destination is finalized

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What the System Does

1. Graph Representation

• Converts a road layout into a weighted graph
• Preserves spatial relationships and connectivity

2. Step-by-Step Computation

• Tracks shortest known distances
• Continuously updates routes as better paths are found

3. Route Optimization

• Produces the lowest-cost path between locations
• Equivalent to navigation system routing behavior

4. Real-World Constraints

• Traffic conditions
• Road closures / one-way systems
• Continuous recalculation

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Part 2 — Instructional Set

How to Find the Shortest Path Using Dijkstra’s Algorithm

Purpose

Manually compute the shortest path between two nodes using a weighted graph.

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Materials

• Weighted graph
• Distance table (Node | Distance | Previous | Status)
• Method for marking visited nodes

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Constraints

• All edge weights must be non-negative
• Graph and table must be visible simultaneously

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Step-by-Step Procedure

Step 1 — Initialize the Table

• Set starting node distance = 0
• Set all other nodes = ∞
• Leave previous nodes blank
• Mark all nodes as unvisited

Check: Only the start node has a known distance

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Step 2 — Select the Current Node

• Choose the unvisited node with the smallest current distance

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Step 3 — Update Neighboring Nodes

For each neighbor:

• Compute:
  new distance = current node distance + edge weight
• If the new distance is smaller, update:
  • Distance
  • Previous node

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Step 4 — Mark Node as Visited

• Mark the current node as finalized
• Do not revisit it

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Step 5 — Repeat

• Return to Step 2
• Continue until the destination node has the smallest distance

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Step 6 — Stop Condition

• Stop when the destination node is selected as the smallest unvisited node

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Step 7 — Trace the Path

• Follow previous nodes backward from destination to start

Output:

• Shortest path
• Total travel cost

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Example Result

Shortest path:
A → B → D → E

Total cost:
11

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Troubleshooting / FAQ

Issue	Cause	Fix
Picking wrong node	Choosing smallest edge instead of smallest total distance	Always compare current distances
Distances stay ∞	Initialization error	Ensure start node = 0
Incorrect final path	Previous nodes not updated correctly	Re-check update step
Algorithm gives wrong result	Negative edge weights	Use a different algorithm (e.g., Bellman-Ford)

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Interactive Component

This project includes:

• Step-by-step algorithm visualization
• Live distance updates
• Practice graph for user application

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Tech Stack

• HTML — structure and diagrams
• CSS — layout and usability design
• JavaScript — algorithm simulation and interaction

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Project Structure

• index.html → Technical description
• instructions.html → Instructional set
• main.css → Styling and layout
• *.js → Interactive behavior

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Summary

This project demonstrates both:

• Conceptual understanding of shortest path algorithms
• Procedural execution through a structured instructional guide

It mirrors how real navigation systems compute and apply optimal routes.