English

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 GG to a fixed digraph HH. We show that if HH admits a weak-near-unanimity polymorphism ϕ\phi then deciding whether GG admits a homomorphism to HH (HOM(HH)) 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.

Keywords

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}
}