Beyond the Worst-Case Analysis of Algorithms (Introduction)
It addresses the problem of algorithm selection for researchers and practitioners by advocating for more nuanced approaches beyond worst-case guarantees.
The paper critiques worst-case analysis for algorithm evaluation, arguing it is insufficient for many fundamental problems and proposes exploring alternative analysis methods.
One of the primary goals of the mathematical analysis of algorithms is to provide guidance about which algorithm is the "best" for solving a given computational problem. Worst-case analysis summarizes the performance profile of an algorithm by its worst performance on any input of a given size, implicitly advocating for the algorithm with the best-possible worst-case performance. Strong worst-case guarantees are the holy grail of algorithm design, providing an application-agnostic certification of an algorithm's robustly good performance. However, for many fundamental problems and performance measures, such guarantees are impossible and a more nuanced analysis approach is called for. This chapter surveys several alternatives to worst-case analysis that are discussed in detail later in the book.