Beyond Worst-Case Analysis

This course is motivated by problems for which the traditional worst-case analysis of algorithms fails to differentiate meaningfully between different solutions, or recommends an intuitively "wrong" solution over the "right" one. This course studies systematically alternatives to traditional worst-case analysis that nevertheless enable rigorous and robust guarantees on the performance of an algorithm. Topics include: instance optimality; smoothed analysis; parameterized analysis and condition numbers; models of data (pseudorandomness, locality, diffuse adversaries, etc.); average-case analysis; robust distributional analysis; resource augmentation; planted and semi-random graph models. Motivating problems will be drawn from online algorithms, online learning, constraint satisfaction problems, graph partitioning, scheduling, linear programming, hashing, machine learning, and auction theory. Prerequisites: CS161 (required). CS261 is recommended but not required.