论文标题

除了对算法的最坏情况分析(简介)

Beyond the Worst-Case Analysis of Algorithms (Introduction)

论文作者

Roughgarden, Tim

论文摘要

算法数学分析的主要目标之一是提供有关哪种算法是解决给定计算问题的“最佳”指导。最差的分析分析总结了算法的性能概况,其最差的性能在给定尺寸的任何输入上,隐含地倡导具有最差的最差性能的算法。最差的保证是算法设计的圣杯,为算法的良好性能提供了应用程序认证。但是,对于许多基本问题和绩效指标,这种保证是不可能的,并且需要采取更细微的分析方法。本章调查了最坏情况分析的几种替代方法,这些替代方法将在本书后面详细讨论。

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.

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