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Dichotomy for Digraph Homomorphism Problems

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arxiv 1701.02409 v5 pith:3DDAGAAQ submitted 2017-01-10 cs.CC cs.DS

Tomás Feder , Jeff Kinne , Ashwin Murali , Arash Rafiey This is my paper · ORCID
classification cs.CCcs.DS
keywords dichotomydigraphhomomorphismadmitsalgorithmalgorithmsapproachbulatov
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abstract

We consider the problem of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$. We show that if $H$ admits a weak-near-unanimity polymorphism $\phi$ then deciding whether $G$ admits a homomorphism to $H$ (HOM($H$)) 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.

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