{"id":"https://openalex.org/W1531141150","doi":"https://doi.org/10.1007/978-3-540-72914-3_4","title":"Wooden Geometric Puzzles: Design and Hardness Proofs","display_name":"Wooden Geometric Puzzles: Design and Hardness Proofs","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1531141150","doi":"https://doi.org/10.1007/978-3-540-72914-3_4","mag":"1531141150"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-72914-3_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72914-3_4","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00224-008-9104-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110902792","display_name":"Hans Wilhelm Alt","orcid":null},"institutions":[{"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":"Helmut Alt","raw_affiliation_strings":["Department of Computer Science, Freie Universit\u00e4t Berlin, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Freie Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032730524","display_name":"Hans L. Bodlaender","orcid":"https://orcid.org/0000-0002-9297-3330"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Hans Bodlaender","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053874521","display_name":"Marc van Kreveld","orcid":"https://orcid.org/0000-0001-8208-3468"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Marc van Kreveld","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083387191","display_name":"G\u00fcnter Rote","orcid":"https://orcid.org/0000-0002-0351-5945"},"institutions":[{"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":false,"raw_author_name":"G\u00fcnter Rote","raw_affiliation_strings":["Department of Computer Science, Freie Universit\u00e4t Berlin, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Freie Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111797638","display_name":"G. Tel","orcid":null},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Gerard Tel","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands","institution_ids":["https://openalex.org/I193662353"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5110902792"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0487704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"44","issue":"2","first_page":"16","last_page":"174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9977999925613403,"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":0.9977999925613403,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9925000071525574,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9692999720573425,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7664780616760254},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6807953119277954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6519326567649841},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5510372519493103},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5394319891929626},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.519881010055542},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5155739188194275},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4682537019252777},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21994444727897644}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7664780616760254},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6807953119277954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6519326567649841},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5510372519493103},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5394319891929626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.519881010055542},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5155739188194275},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4682537019252777},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21994444727897644},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1007/978-3-540-72914-3_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72914-3_4","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":"doi:10.1007/s00224-008-9104-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-008-9104-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-008-9104-3.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.111.4672","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.4672","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.inf.fu-berlin.de/~rote/Papers/pdf-gzipped/Wooden+geometric+puzzles:+design+and+hardness+proofs.pdf.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.3028","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.3028","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uu.nl/research/techreps/repo/CS-2007/2007-009.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.79.3709","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.79.3709","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uu.nl/research/techreps/repo/CS-2007/2007-009.ps.gz","raw_type":"text"},{"id":"pmh:oai:dspace.library.uu.nl:1874/29974","is_oa":true,"landing_page_url":"http://dspace.library.uu.nl:8080/handle/1874/29974","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/22187","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/22187","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"UU-CS, 2007-009. Utrecht University","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/29974","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/29974","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theory of Computing Systems. Springer","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:1531141150","is_oa":false,"landing_page_url":"https://dspace.library.uu.nl/bitstream/1874/22187/1/2007-009.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s00224-008-9104-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-008-9104-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-008-9104-3.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1531141150.pdf","grobid_xml":"https://content.openalex.org/works/W1531141150.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2032056620","https://openalex.org/W2034604437","https://openalex.org/W2081747232","https://openalex.org/W2087818742","https://openalex.org/W2115330428","https://openalex.org/W2160080538"],"related_works":["https://openalex.org/W2175385586","https://openalex.org/W1964331290","https://openalex.org/W2149951504","https://openalex.org/W3170426943","https://openalex.org/W1603553157","https://openalex.org/W1682147331","https://openalex.org/W2888250735","https://openalex.org/W3016931611","https://openalex.org/W3033804366","https://openalex.org/W1584515386","https://openalex.org/W2153715991","https://openalex.org/W59759164","https://openalex.org/W3162278033","https://openalex.org/W2810215715","https://openalex.org/W2159783982","https://openalex.org/W2096390054","https://openalex.org/W2624065397","https://openalex.org/W1975452925","https://openalex.org/W3210048346","https://openalex.org/W3134818819"],"abstract_inverted_index":{"We":[0,64,88],"discuss":[1],"some":[2],"new":[3],"geometric":[4],"puzzles":[5,17,20,32],"and":[6,18,60],"the":[7,29,50,85],"complexity":[8],"of":[9,24,31,54,68,91],"their":[10],"extension":[11],"to":[12,34,43,49],"arbitrary":[13],"sizes.":[14],"For":[15],"gate":[16],"two-layer":[19],"we":[21],"prove":[22],"NP-completeness":[23],"solving":[25],"them.":[26],"Not":[27],"only":[28,58],"solution":[30],"leads":[33,48],"interesting":[35,44],"questions,":[36],"but":[37],"also":[38,77],"puzzle":[39],"design":[40],"gives":[41],"rise":[42],"theoretical":[45],"questions.":[46],"This":[47,75],"search":[51],"for":[52,79,101],"instances":[53,67,90],"partition":[55,80],"that":[56,66],"use":[57],"integers":[59,93],"are":[61],"uniquely":[62],"solvable.":[63],"show":[65],"polynomial":[69],"size":[70],"exist":[71],"with":[72,84,94],"this":[73],"property.":[74],"result":[76],"holds":[78],"into":[81],"k":[82,98],"subsets":[83],"same":[86],"sum:":[87],"construct":[89],"n":[92],"subset":[95],"sum":[96],"O(n":[97],"+":[99],"1),":[100],"fixed":[102],"k.":[103]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}
