Going beyond worst-case analysis using predictions
Abstract
The theoretical study of algorithms and data structures has been bolstered by worst-case analysis, where we prove bounds on the running time, space, approximation ratio, competitive ratio, or other measure that holds even in the worst case. Worst-case analysis has proven invaluable for understanding aspects of both the complexity and practicality of algorithms, providing useful features like the ability to use algorithms as building blocks and subroutines with a clear picture of the worst-case performance. More and more, however, the limitations of worst-case analysis become apparent and create new challenges. In practice, we often do not face worst-case scenarios, and the question arises of how we can tune our algorithms to work even better on the kinds of instances we are likely to see, while ideally keeping a rigorous formal framework similar to what we have developed through worst-case analysis.
We examine a recent trend that develops algorithms parameterized by additional parameters which capture "the kinds of instances we are likely to see," and obtains a finer grained analysis of algorithms' performance. We will give examples of re-analyzing classical algorithms through this lens, as well as developing new algorithms that expose new structural insights about the problems.
Based on work with Kareem Amin, Travis Dick, Michael Dinitz, Sungjin Im, Misha Khodak, Silvio Lattanzi, Thomas Lavastida, Thodoris Lykouris, and Andres Munoz Medina
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