Why Linear Programming cannot solve large instances of NP-complete problems in polynomial time
Computational Complexity
2025-10-20 v1 Discrete Mathematics
Data Structures and Algorithms
Numerical Analysis
Numerical Analysis
Abstract
This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial time, what places them in P class. During past three years there appeared some articles using LP to solve NP-complete problems. This methods use large number of variables (O(n^9)) solving correctly almost all instances that can be solved in reasonable time. Can they solve infinitively large instances? This article gives answer to this question.
Keywords
Cite
@article{arxiv.cs/0611008,
title = {Why Linear Programming cannot solve large instances of NP-complete problems in polynomial time},
author = {Radoslaw Hofman},
journal= {arXiv preprint arXiv:cs/0611008},
year = {2025}
}