{"id":"https://openalex.org/W2136139362","doi":"https://doi.org/10.1007/978-3-642-14031-0_29","title":"Tile-Packing Tomography Is ${\\mathbb{NP}}$ -hard","display_name":"Tile-Packing Tomography Is ${\\mathbb{NP}}$ -hard","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2136139362","doi":"https://doi.org/10.1007/978-3-642-14031-0_29","mag":"2136139362"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-14031-0_29","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-14031-0_29","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024529572","display_name":"Marek Chrob\u00e1k","orcid":"https://orcid.org/0000-0002-8673-2709"},"institutions":[{"id":"https://openalex.org/I1311060795","display_name":"U.S. National Science Foundation","ror":"https://ror.org/021nxhr62","country_code":"US","type":"government","lineage":["https://openalex.org/I1311060795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marek Chrobak","raw_affiliation_strings":["Department of Computer Science, University of California, Research partially supported by National Science Foundation, grant CCF-0729071, Riverside, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Research partially supported by National Science Foundation, grant CCF-0729071, Riverside, USA","institution_ids":["https://openalex.org/I1311060795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029270613","display_name":"Christoph D\u00fcrr","orcid":"https://orcid.org/0000-0001-8103-5333"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christoph D\u00fcrr","raw_affiliation_strings":["CNRS and Lab. of Computer Science of the Ecole Polytechnique, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS and Lab. of Computer Science of the Ecole Polytechnique, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I142476485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073450696","display_name":"Flavio Gu\u00ed\u00f1ez","orcid":null},"institutions":[{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Flavio Gu\u00ed\u00f1ez","raw_affiliation_strings":["DIM, Universidad de Chile, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DIM, Universidad de Chile, Chile","institution_ids":["https://openalex.org/I69737025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033558235","display_name":"Antoni Lozano","orcid":"https://orcid.org/0000-0002-3633-063X"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antoni Lozano","raw_affiliation_strings":["Technical University of Catalonia, Research partially supported by CICYT projects TIN2007-68005-C04-03 and TIN2008-06582-C03-01, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Catalonia, Research partially supported by CICYT projects TIN2007-68005-C04-03 and TIN2008-06582-C03-01, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077796278","display_name":"Nguy\u1ec5n Kim Th\u1eafng","orcid":"https://orcid.org/0000-0002-6085-9453"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Nguyen Kim Thang","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Denmark","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2079646,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"254","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tile","display_name":"Tile","score":0.9429200291633606},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7549452781677246},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.589507520198822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5874876379966736},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5567641258239746},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5105339288711548},{"id":"https://openalex.org/keywords/packing-problems","display_name":"Packing problems","score":0.49201223254203796},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47811001539230347},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3860780894756317},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3415672779083252},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3109307885169983},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3095460832118988}],"concepts":[{"id":"https://openalex.org/C2780728851","wikidata":"https://www.wikidata.org/wiki/Q468402","display_name":"Tile","level":2,"score":0.9429200291633606},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7549452781677246},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.589507520198822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5874876379966736},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5567641258239746},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5105339288711548},{"id":"https://openalex.org/C130253271","wikidata":"https://www.wikidata.org/wiki/Q3851477","display_name":"Packing problems","level":2,"score":0.49201223254203796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47811001539230347},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3860780894756317},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3415672779083252},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3109307885169983},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3095460832118988},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-642-14031-0_29","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-14031-0_29","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pure.atira.dk:publications/c30f537f-9d43-49ba-ab5d-42ecdbfe30e1","is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/c30f537f-9d43-49ba-ab5d-42ecdbfe30e1","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Chrobak, M, D\u00fcrr, C, Gu\u00ed\u00f1ez, F, Lozano, A & Thang, N K 2010, 'Tile-Packing Tomography Is NP-hard', Lecture Notes in Computer Science, vol. 6196, pp. 254-263. https://doi.org/10.1007/978-3-642-14031-0_29","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/16114","is_oa":false,"landing_page_url":"http://hdl.handle.net/2117/16114","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W191340782","https://openalex.org/W617403369","https://openalex.org/W1491188970","https://openalex.org/W1704269950","https://openalex.org/W1974451757","https://openalex.org/W1982979061","https://openalex.org/W1992033079","https://openalex.org/W2022252334","https://openalex.org/W2056122464","https://openalex.org/W2060448518","https://openalex.org/W2069438720","https://openalex.org/W4243285511"],"related_works":["https://openalex.org/W2114959296","https://openalex.org/W38346124","https://openalex.org/W2502442966","https://openalex.org/W2138666621","https://openalex.org/W2383936314","https://openalex.org/W1992771654","https://openalex.org/W2022661278","https://openalex.org/W2777914781","https://openalex.org/W4293505982","https://openalex.org/W2951541105"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}