Advanced Algorithm Design

This unit explores advanced algorithmic strategies, data structures, and optimization techniques used to solve complex computational problems efficiently. Students will study problem reductions, graph and matrix methods, randomized and streaming approaches, and implementation considerations including hardware acceleration to prepare for applied algorithm projects in the final unit.

Learning Objectives

• Analyze time, space, and correctness trade-offs for advanced algorithmic techniques including divide-and-conquer, recursion, greedy methods, randomized algorithms, and problem reductions (e.g., 3SUM to MST).
• Apply appropriate data structures and algorithmic primitives—such as trees, hashing, graphs, sketches, and matrix operations—to design and implement efficient solutions for problems like PageRank, path finding, SAT satisfiability checks, and streaming queries.
• Demonstrate optimization and performance engineering skills by implementing algorithmic improvements (fast matrix multiplication, parallelization, and hardware acceleration) and measuring their impact on real workloads.
• Evaluate multiple solution strategies using empirical benchmarks and heuristic criteria to select approaches that meet constraints on accuracy, memory, and runtime for given problem instances.