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Course Description. Analysis of correctness and complexity of various efficient algorithms; discussion of problems for which no efficient solutions are known.

Focus: Beyond Worst-case Algorithm Analysis: While worst-case analysis provides robust guarantees by considering the absolute worst possible input for an algorithm, it often fails to explain the empirical success of algorithms in practice, particularly for problems where the worst-case scenario is rare or unrealistic. Beyond worst-case algorithm analysis is focused on methods to beat the worst-case analysis by taking advantage of input properties that occur in practice.

Coursework. Coursework will consist of in-class participation, homework assignments, two in-class midterm exams, and a final exam. The final grade will be computed based on 10% for in-class participation, 10% for homework assignments, 25% for each midterm exam, and 30% for the final exam. In computing the final score, the lowest homework score will be dropped, and the lowest 3 in-class participation scores will be dropped.

Academic honesty policy. Collaboration on exams is not allowed and each exam must be an individual effort. Working with others on homework assignments is allowed, provided it is acknowledged. The use of generative AI tools for any purpose other than to improve writing (e.g., to improve spelling and/or grammar) is prohibited unless specifically allowed. In addition to the procedures of the ICS Cheating Policy, students caught cheating will be given a failing grade for the assessment in question.

Recommended Textbooks:

• Beyond the Worst-Case Analysis of Algorithms, edited by Tim Roughgarden, 2020, Cambridge University Press.
• Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis, Second edition, by Mitzenmacher and Upfal, 2017, Cambridge University Press.
• Parameterized Algorithms, by Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, Saurabh, 2016, Springer.

Tentative Schedule

1. Introduction to beyond worst-case algorithm analysis
2. Amortized analysis
3. Randomized algorithms
4. Instance sensitivity
5. Fixed parameter tractability
6. Learning-augmented algorithm design