A Polynomial Time Algorithm For 0-1 Integer Linear Programmings
Abstract
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a strong cut. Then the solution algorithm of a 0-1 ILP is developed based on the new constraints. Algorithmic complexity analysis shows that the proposed algorithm is a polynomial-time algorithm, which means that P=NP.
Cite
@article{arxiv.2302.06049,
title = {A Polynomial Time Algorithm For 0-1 Integer Linear Programmings},
author = {G. Q. Zhang},
journal= {arXiv preprint arXiv:2302.06049},
year = {2023}
}
Comments
After testing, this is not a polynomial time algorithm for 0-1 ILP. The reason is that the new constraints generated by arbitrarily finding r different AVs may not necessarily be equivalent to the original constraint.That is to say, it is currently not possible to generate a new constraint equivalent to the original constraint in polynomial time