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- W4307769354 abstract "We find an orientation of a tree with 20 vertices such that the corresponding fixed-template constraint satisfaction problem (CSP) is NP-complete, and prove that for every orientation of a tree with fewer vertices the corresponding CSP can be solved in polynomial time. We also compute the smallest tree that is NL-hard (assuming L is not NL), the smallest tree that cannot be solved by arc consistency, and the smallest tree that cannot be solved by Datalog. Our experimental results also support a conjecture of Bulin concerning a question of Hell, Nesetril and Zhu, namely that easy trees lack the ability to count. Most proofs are computer-based and make use of the most recent universal-algebraic theory about the complexity of finite-domain CSPs. However, further ideas are required because of the huge number of orientations of trees. In particular, we use the well-known fact that it suffices to study orientations of trees that are cores and show how to efficiently decide whether a given orientation of a tree is a core using the arc-consistency procedure. Moreover, we present a method to generate orientations of trees that are cores that works well in practice. In this way we found interesting examples for the open research problem to classify finite-domain CSPs in NL." @default.
- W4307769354 created "2022-11-05" @default.
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- W4307769354 date "2022-05-16" @default.
- W4307769354 modified "2023-09-27" @default.
- W4307769354 title "The Smallest Hard Trees" @default.
- W4307769354 doi "https://doi.org/10.48550/arxiv.2205.07528" @default.
- W4307769354 hasPublicationYear "2022" @default.
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