{"id":"https://openalex.org/W4237656710","doi":"https://doi.org/10.1007/3-540-51486-4_76","title":"Testing approximate symmetry in the plane is NP-hard","display_name":"Testing approximate symmetry in the plane is NP-hard","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W4237656710","doi":"https://doi.org/10.1007/3-540-51486-4_76"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-51486-4_76","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51486-4_76","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/A5063423540","display_name":"Sebastian Iwanowski","orcid":null},"institutions":[{"id":"https://openalex.org/I2800345347","display_name":"Berlin Mathematical School","ror":"https://ror.org/03zekj455","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800345347"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sebastian Iwanowski","raw_affiliation_strings":["Fachbereich Mathematik, Arnimallee 2-6, D-1000, Berlin (West) 33, Germany","Freie Universit\u00e4t Berlin, Germany","Fachbereich Mathematik, Berlin (West) 33, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Arnimallee 2-6, D-1000, Berlin (West) 33, Germany","institution_ids":["https://openalex.org/I2800345347"]},{"raw_affiliation_string":"Freie Universit\u00e4t Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Fachbereich Mathematik, Berlin (West) 33, Germany","institution_ids":["https://openalex.org/I2800345347"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063423540"],"corresponding_institution_ids":["https://openalex.org/I2800345347","https://openalex.org/I75951250"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.5423,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66860465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"291","last_page":"304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9940999746322632,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6251538395881653},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.539534330368042},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5332821011543274},{"id":"https://openalex.org/keywords/plane-symmetry","display_name":"Plane symmetry","score":0.5138378739356995},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.4733310341835022},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45939183235168457},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.45034804940223694},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.45010656118392944},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.43614423274993896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42209795117378235},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4116588830947876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3941729664802551},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35289621353149414},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14823263883590698},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11044386029243469},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08217906951904297}],"concepts":[{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6251538395881653},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.539534330368042},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5332821011543274},{"id":"https://openalex.org/C40425006","wikidata":"https://www.wikidata.org/wiki/Q7201020","display_name":"Plane symmetry","level":2,"score":0.5138378739356995},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.4733310341835022},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45939183235168457},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.45034804940223694},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.45010656118392944},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.43614423274993896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42209795117378235},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4116588830947876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3941729664802551},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35289621353149414},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14823263883590698},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11044386029243469},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08217906951904297},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-51486-4_76","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51486-4_76","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1765849099","https://openalex.org/W1986145324","https://openalex.org/W2004759101","https://openalex.org/W2036429506","https://openalex.org/W2049621921","https://openalex.org/W2066577300","https://openalex.org/W2079909954","https://openalex.org/W2082205964","https://openalex.org/W4232428446"],"related_works":["https://openalex.org/W3198453818","https://openalex.org/W3120430178","https://openalex.org/W3137373926","https://openalex.org/W2953203706","https://openalex.org/W2347888409","https://openalex.org/W2318011843","https://openalex.org/W2003579177","https://openalex.org/W4386720101","https://openalex.org/W189530215","https://openalex.org/W2081220546"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}