We determine the complexity of all constraint satisfaction problems over partial orders, in particular we show that every such problem is NP-complete or can be solved in polynomial time. This result generalises the complexity dichotomy for temporal constraint satisfaction problems by Bodirsky and Kára. We apply the so called universal-algebraic approach together with tools from model theory and Ramsey theory to prove our result. In the course of this analysis we also establish a structural dichotomy regarding the model theoretic properties of the reducts of the random partial order.
@InProceedings{kompatscher_et_al:LIPIcs.STACS.2017.47, author = {Kompatscher, Michael and Pham, Trung Van}, title = {{A Complexity Dichotomy for Poset Constraint Satisfaction}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {47:1--47:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.47}, URN = {urn:nbn:de:0030-drops-69850}, doi = {10.4230/LIPIcs.STACS.2017.47}, annote = {Keywords: Constraint Satisfaction, Random Partial Order, Computational Complexity, Universal Algebra, Ramsey Theory} }
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