Beyond the Worst-Case Analysis of Algorithms (Introduction)

TL;DR

This paper discusses limitations of worst-case analysis in algorithms and explores alternative approaches for performance evaluation that provide more nuanced insights beyond worst-case guarantees.

Contribution

It surveys various alternative analysis methods to worst-case analysis, highlighting their importance for understanding algorithm performance in practical scenarios.

Findings

Worst-case analysis can be overly pessimistic for many problems.

Alternative analysis methods offer more realistic performance insights.

The chapter emphasizes the need for nuanced evaluation approaches.

Abstract

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.