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Shellability is NP-complete
Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. 2018. Shellability is NP-complete. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 41:1-41:16.
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Leibniz International Proceedings in Information, LIPIcs
Abstract
We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes.
Publishing Year
Date Published
2018-06-11
Acknowledgement
Partially supported by the project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM) of Czech-French collaboration.
Volume
99
Page
41:1 - 41:16
Conference
SoCG: Symposium on Computational Geometry
Conference Location
Budapest, Hungary
Conference Date
2018-06-11 – 2018-06-14
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Cite this
Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. Shellability is NP-complete. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:41:1-41:16. doi:10.4230/LIPIcs.SoCG.2018.41
Goaoc, X., Paták, P., Patakova, Z., Tancer, M., & Wagner, U. (2018). Shellability is NP-complete (Vol. 99, p. 41:1-41:16). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.41
Goaoc, Xavier, Pavel Paták, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Shellability Is NP-Complete,” 99:41:1-41:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.41.
X. Goaoc, P. Paták, Z. Patakova, M. Tancer, and U. Wagner, “Shellability is NP-complete,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 41:1-41:16.
Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. 2018. Shellability is NP-complete. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 41:1-41:16.
Goaoc, Xavier, et al. Shellability Is NP-Complete. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 41:1-41:16, doi:10.4230/LIPIcs.SoCG.2018.41.
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