{"date_updated":"2023-09-06T11:10:58Z","publication_identifier":{"issn":["0004-5411"]},"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."}],"date_published":"2019-06-01T00:00:00Z","department":[{"_id":"UlWa"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.1145/3314024","oa":1,"intvolume":"        66","author":[{"last_name":"Goaoc","first_name":"Xavier","full_name":"Goaoc, Xavier"},{"first_name":"Pavel","full_name":"Patak, Pavel","last_name":"Patak","id":"B593B804-1035-11EA-B4F1-947645A5BB83"},{"last_name":"Patakova","full_name":"Patakova, Zuzana","first_name":"Zuzana","orcid":"0000-0002-3975-1683","id":"48B57058-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Martin","full_name":"Tancer, Martin","last_name":"Tancer"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","last_name":"Wagner","full_name":"Wagner, Uli","first_name":"Uli"}],"article_processing_charge":"No","oa_version":"Preprint","issue":"3","type":"journal_article","day":"01","isi":1,"scopus_import":"1","status":"public","article_type":"original","volume":66,"_id":"7108","publication":"Journal of the ACM","external_id":{"arxiv":["1711.08436"],"isi":["000495406300007"]},"date_created":"2019-11-26T10:13:59Z","title":"Shellability is NP-complete","article_number":"21","language":[{"iso":"eng"}],"month":"06","publication_status":"published","quality_controlled":"1","publisher":"ACM","main_file_link":[{"url":"https://arxiv.org/pdf/1711.08436.pdf","open_access":"1"}],"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>","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>.","ista":"Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. 2019. Shellability is NP-complete. Journal of the ACM. 66(3), 21.","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>.","short":"X. Goaoc, P. Patak, Z. Patakova, M. Tancer, U. Wagner, Journal of the ACM 66 (2019).","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>"},"year":"2019","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"184"}]}}