Advanced Algorithmic Techniques

This unit explores advanced algorithm design patterns, data structures, and performance strategies for solving practical and theoretical problems in programming and software development. Students will study graph and tree algorithms, hashing and sketching for streams, randomization, recursion, matrix methods, reductions (e.g., to SAT and MST), and hardware acceleration to prepare for capstone projects and applied optimization tasks.

Learning Objectives

• Analyze time, space, and correctness trade-offs for advanced algorithms including 3SUM solutions, greedy strategies, recursion-based methods, graph algorithms (MST, PageRank, path finding), and matrix multiplication improvements
• Apply appropriate data structures and techniques—trees, hashing, sketches, graphs, and matrix representations—to implement solutions for streaming, search, and optimization problems and validate them with test cases
• Demonstrate use of randomization, heuristic search, reductions (e.g., SAT and MST), and hardware acceleration (e.g., parallelism/SIMD/GPU) to improve performance and measure empirical speedups
• Evaluate and justify selection among exact, approximate, and heuristic approaches for large-scale or constrained problems by comparing complexity analyses, empirical results, and memory/accuracy trade-offs