{"alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"quality_controlled":"1","title":"Shellability is NP-complete","related_material":{"record":[{"status":"public","relation":"later_version","id":"7108"}]},"status":"public","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","scopus_import":1,"oa":1,"oa_version":"Published Version","date_created":"2018-12-11T11:45:04Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"}],"abstract":[{"text":"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.","lang":"eng"}],"date_published":"2018-06-11T00:00:00Z","publication_status":"published","month":"06","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2023-09-06T11:10:57Z","file":[{"date_created":"2018-12-17T16:35:02Z","file_size":718414,"file_id":"5725","date_updated":"2020-07-14T12:45:18Z","access_level":"open_access","creator":"dernst","file_name":"2018_LIPIcs_Goaoc.pdf","content_type":"application/pdf","checksum":"d12bdd60f04a57307867704b5f930afd","relation":"main_file"}],"type":"conference","day":"11","ddc":["516","000"],"acknowledgement":"Partially supported by the project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM) of Czech-French collaboration.","file_date_updated":"2020-07-14T12:45:18Z","year":"2018","intvolume":"        99","publist_id":"7736","volume":99,"language":[{"iso":"eng"}],"_id":"184","citation":{"mla":"Goaoc, Xavier, et al. <i>Shellability Is NP-Complete</i>. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 41:1-41:16, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.41\">10.4230/LIPIcs.SoCG.2018.41</a>.","ieee":"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.","ista":"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.","apa":"Goaoc, X., Paták, P., Patakova, Z., Tancer, M., &#38; 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. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.41\">https://doi.org/10.4230/LIPIcs.SoCG.2018.41</a>","chicago":"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. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.41\">https://doi.org/10.4230/LIPIcs.SoCG.2018.41</a>.","ama":"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:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.41\">10.4230/LIPIcs.SoCG.2018.41</a>","short":"X. Goaoc, P. Paták, Z. Patakova, M. Tancer, U. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 41:1-41:16."},"conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2018-06-11","location":"Budapest, Hungary","end_date":"2018-06-14"},"doi":"10.4230/LIPIcs.SoCG.2018.41","page":"41:1 - 41:16","author":[{"first_name":"Xavier","last_name":"Goaoc","full_name":"Goaoc, Xavier"},{"full_name":"Paták, Pavel","first_name":"Pavel","last_name":"Paták"},{"orcid":"0000-0002-3975-1683","last_name":"Patakova","first_name":"Zuzana","id":"48B57058-F248-11E8-B48F-1D18A9856A87","full_name":"Patakova, Zuzana"},{"orcid":"0000-0002-1191-6714","last_name":"Tancer","first_name":"Martin","full_name":"Tancer, Martin","id":"38AC689C-F248-11E8-B48F-1D18A9856A87"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568"}],"has_accepted_license":"1"}