Assuming that P is not equal to NP, the worst-case run time of any algorithm solving an NP-complete problem must be super-polynomial. But what is the fastest run time we can get? Before one can even hope to approach this question, a more provocative question presents itself: Since for many problems the naive brute-force baseline algorithms are still the fastest ones, maybe their run times are already optimal? The area that we call in this survey "fine-grained complexity of NP-complete problems" studies exactly this question. We invite the reader to catch up on selected classic results as well as delve into exciting recent developments in a riveting tour through the area passing by (among others) algebra, complexity theory, extremal and additive combinatorics, cryptography, and, of course, last but not least, algorithm design.

翻译：假设P不等于NP，任何求解NP完全问题的算法在最坏情况下的运行时间都必须是超多项式的。但我们可以获得的最快运行时间是多少？在人们甚至有望探讨这个问题之前，一个更具挑战性的问题已然浮现：既然对于许多问题，朴素的暴力基线算法仍然是最快的，也许它们的运行时间已经是最优的？我们在本综述中称为“NP完全问题的细粒度复杂性”的领域，正是研究这一问题的。我们邀请读者通过一次引人入胜的领域巡览，回顾选定的经典成果并深入探讨激动人心的最新进展，沿途将经过（其中包括）代数、复杂性理论、极值与加法组合学、密码学，当然，最后但同样重要的是，算法设计。