Computer Science > Computational Complexity
[Submitted on 28 Sep 2020 (v1), last revised 23 Nov 2020 (this version, v2)]
Title:Digraph homomorphism problem and weak near unanimity polymorphism
View PDFAbstract: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 proof of the dichotomy conjecture (now dichotomy theorem) by Feder and Vardi. Our approach is combinatorial, and it is simpler than the two algorithms found by Bulatov and Zhuk. We have implemented our algorithm and show some experimental results. We use our algorithm together with the recent result [38] for recognition of Maltsev polymorphisms and decide in polynomial time if a given relational structure $\mathcal{R}$ admits a weak near unanimity polymorphism.
Submission history
From: Arash Rafiey [view email][v1] Mon, 28 Sep 2020 06:17:36 UTC (130 KB)
[v2] Mon, 23 Nov 2020 01:43:02 UTC (919 KB)
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