Shortest Path Routing Algorithm || Dijkstra's algorithm || Computer Networks

Dijkstra's Algorithm Overview
📌 The core aim of the Dijkstra's algorithm (also known as the shortest path rooting algorithm) is to find the shortest path from a Source router (node) to a Destination router (node) in a graph.
⚙️ The graph consists of nodes (routers, labeled A, B, C, etc.) and edges (communication links) whose associated numbers represent the distance, cost, weight, or delay.
♾️ Nodes are classified into three types: Tentative (white circle), Current Working Node (represented by a $\Psi$ symbol), and Permanent (solid circle).

Algorithm Steps and Node Evaluation
1️⃣ Initialization: Set the Source node as the Current Working Node and mark it as Permanent (solid circle). All other nodes start as Tentative.
2️⃣ Exploration: Explore the neighbors of the current working node, updating their path lengths (cost/predecessor) if a shorter path is found. Path length is tracked as (Cost, Predecessor Node).
3️⃣ Selection: Among all Tentative nodes, select the one with the smallest current path length and designate it as the new Current Working Node, then mark it as Permanent.
4️⃣ Path Update Example: In the demonstration, traveling from A to B costs 2 (updated as 2, A). When updating G, its cost changes from 6 (via A) to 5 (via E), as $5 < 6$.
5️⃣ Termination: The process repeats until the Destination node is marked as Permanent, allowing the shortest path to be traced back via the recorded predecessors.

Key Points & Insights
➡️ The algorithm iteratively builds the shortest path tree by always selecting the tentative node with the minimum known distance.
➡️ If a newly calculated path length is less than the previously recorded length for a node, the path information (cost and predecessor) must be updated (e.g., updating G's cost from 6 to 5).
➡️ Path lengths for unknown nodes are initially set to infinity ($\infty$) with an unknown predecessor (represented by a hyphen/minus sign).
➡️ The final shortest path from A to D found in the example trace was: A $\rightarrow$ B $\rightarrow$ E $\rightarrow$ F $\rightarrow$ H $\rightarrow$ D, with a total cost calculation shown as $2+2+2+2+2+2$ (Total cost calculation involves summing the edge weights along the path).

📸 Video summarized with SummaryTube.com on Feb 02, 2026, 01:36 UTC