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arXiv · 2601.05044

An Invitation to "Fine-grained Complexity of NP-Complete Problems"

Jesper Nederlof
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Abstract

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.

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Jesper Nederlof. 2026-01-08. An Invitation to "Fine-grained Complexity of NP-Complete Problems". https://arxiv.org/abs/2601.05044

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