{"language":[{"iso":"eng"}],"author":[{"last_name":"Goaoc","first_name":"Xavier","full_name":"Goaoc, Xavier"},{"id":"B593B804-1035-11EA-B4F1-947645A5BB83","last_name":"Patak","first_name":"Pavel","full_name":"Patak, Pavel"},{"last_name":"Patakova","id":"48B57058-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3975-1683","first_name":"Zuzana","full_name":"Patakova, Zuzana"},{"full_name":"Tancer, Martin","first_name":"Martin","last_name":"Tancer"},{"orcid":"0000-0002-1494-0568","first_name":"Uli","full_name":"Wagner, Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"UlWa"}],"publication":"Journal of the ACM","article_number":"21","date_created":"2019-11-26T10:13:59Z","year":"2019","article_processing_charge":"No","date_published":"2019-06-01T00:00:00Z","_id":"7108","doi":"10.1145/3314024","publication_identifier":{"issn":["0004-5411"]},"month":"06","issue":"3","title":"Shellability is NP-complete","oa_version":"Preprint","citation":{"apa":"Goaoc, X., Patak, P., Patakova, Z., Tancer, M., &#38; Wagner, U. (2019). Shellability is NP-complete. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/3314024\">https://doi.org/10.1145/3314024</a>","short":"X. Goaoc, P. Patak, Z. Patakova, M. Tancer, U. Wagner, Journal of the ACM 66 (2019).","ieee":"X. Goaoc, P. Patak, Z. Patakova, M. Tancer, and U. Wagner, “Shellability is NP-complete,” <i>Journal of the ACM</i>, vol. 66, no. 3. ACM, 2019.","mla":"Goaoc, Xavier, et al. “Shellability Is NP-Complete.” <i>Journal of the ACM</i>, vol. 66, no. 3, 21, ACM, 2019, doi:<a href=\"https://doi.org/10.1145/3314024\">10.1145/3314024</a>.","chicago":"Goaoc, Xavier, Pavel Patak, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Shellability Is NP-Complete.” <i>Journal of the ACM</i>. ACM, 2019. <a href=\"https://doi.org/10.1145/3314024\">https://doi.org/10.1145/3314024</a>.","ama":"Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. Shellability is NP-complete. <i>Journal of the ACM</i>. 2019;66(3). doi:<a href=\"https://doi.org/10.1145/3314024\">10.1145/3314024</a>","ista":"Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. 2019. Shellability is NP-complete. Journal of the ACM. 66(3), 21."},"type":"journal_article","publisher":"ACM","scopus_import":"1","oa":1,"publication_status":"published","main_file_link":[{"url":"https://arxiv.org/pdf/1711.08436.pdf","open_access":"1"}],"related_material":{"record":[{"relation":"earlier_version","id":"184","status":"public"}]},"intvolume":"        66","date_updated":"2023-09-06T11:10:58Z","abstract":[{"lang":"eng","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. Another simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-shellable."}],"status":"public","day":"01","quality_controlled":"1","external_id":{"isi":["000495406300007"],"arxiv":["1711.08436"]},"article_type":"original","volume":66,"isi":1}