Dichotomy for Digraph Homomorphism Problems
Computational Complexity
2020-08-11 v5 Data Structures and Algorithms
Abstract
We consider the problem of finding a homomorphism from an input digraph to a fixed digraph . We show that if admits a weak-near-unanimity polymorphism then deciding whether admits a homomorphism to (HOM()) is polynomial time solvable? This gives a proof of the dichotomy conjecture (now dichotomy theorem) by Feder and Vardi [29]. Our approach is combinatorial, and it is simpler than the two algorithms found by Bulatov [9] and Zhuk [46] in 2017. We have implemented our algorithm and show some experimental results.
Cite
@article{arxiv.1701.02409,
title = {Dichotomy for Digraph Homomorphism Problems},
author = {Tomás Feder and Jeff Kinne and Ashwin Murali and Arash Rafiey},
journal= {arXiv preprint arXiv:1701.02409},
year = {2020}
}