# Linearly-growing Reductions of Karp's 21 NP-complete Problems

arXiv: https://arxiv.org/abs/1902.10349 · HTML: https://mlsanity.com/paper/1902.10349/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 1 of 1)

- [Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?](https://mlsanity.com/paper/2603.02462/) (2026)

## Abstract (arXiv)

We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete problems contains a kernel subset of six problems with the property that each problem in the larger set can be converted to one of these six problems with only linear growth in problem size. This finding has potential applications in optimisation theory because the kernel subset includes 0-1 integer programming, job sequencing and undirected Hamiltonian cycle problems.