Advanced Algorithms and Applications

This unit synthesizes graph algorithms, algorithmic analysis, compression, cryptography, and computational decision problems to address real-world data and security challenges. Students build numeric representations of relations, implement and evaluate techniques for routing, ranking, compression, edit distance optimization, and large-number arithmetic, and apply cryptographic primitives and ethical considerations for automation and spatial issues to prepare for capstone work or further CS study.

Learning Objectives

• Analyze graph-structured data by converting relations into numeric formats (e.g., adjacency lists/matrices), interpreting link-analysis measures (such as PageRank and centrality), and applying spatial reasoning to support routing and proximity queries
• Apply algorithmic techniques to compute shortest paths, optimize edit-distance calculations, perform data compression, and multiply very large numbers, selecting appropriate data-domain transformations and implementations for given problem constraints
• Demonstrate secure-data techniques by implementing basic encryption, one-way functions, parity checks, and unique-identifier schemes while managing automation behaviors and protecting secret data in practical applications
• Evaluate algorithms and systems for correctness, decidability (including halting considerations), time/space complexity, empirical performance, and fairness (e.g., resource division), and justify design choices with quantitative and ethical analyses