Developed DFS algorithms for network connectivity

📅 2023-10-09 — Session: Developed DFS algorithms for network connectivity

🕒 05:00–05:55
🏷️ Labels: DFS, Algorithms, Graph Theory, Optimization, Memoization
📂 Project: Dev
⭐ Priority: MEDIUM

Session Goal

The session aimed to explore and develop algorithms using Depth-First Search (DFS) to determine network connectivity and identify critical disconnections or ‘bridges’ in graph structures.

Key Activities

• DFS Algorithms for Network Connectivity: Detailed the implementation of two DFS-based algorithms to assess network connectivity and identify isolated nodes due to attacks, with a time complexity of O(|C|).
• Bridge Identification in Graphs: Explained the process of identifying critical edges or ‘bridges’ in a graph that, if removed, would increase the number of connected components. This was achieved by using a DFS-based approach, improving efficiency over executing multiple DFS runs.
• Complexity Analysis: Provided a detailed breakdown of the algorithm’s complexity, focusing on the use of discovery and low arrays to determine back cycles and bridge conditions.
• Optimization of amigos_debajo Function: Discussed and implemented memoization to optimize the amigos_debajo function, reducing redundant calculations and improving performance.
• Pseudocode Development: Developed pseudocode for calculating friends beneath a node in a DFS tree, utilizing set operations for efficient combination of child nodes’ friends.

Achievements

• Successfully implemented and analyzed DFS algorithms for network connectivity and bridge identification.
• Optimized existing functions using memoization techniques.
• Developed clear pseudocode for recursive DFS operations.

Pending Tasks

• Further testing and validation of the optimized amigos_debajo function in different graph scenarios.
• Exploration of additional optimization techniques for DFS algorithms.