{"id":"https://openalex.org/W1593052729","doi":"https://doi.org/10.1007/bfb0024482","title":"Gadgets, approximation, and linear programming: Improved hardness results for cut and satisfiability problems","display_name":"Gadgets, approximation, and linear programming: Improved hardness results for cut and satisfiability problems","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1593052729","doi":"https://doi.org/10.1007/bfb0024482","mag":"1593052729"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0024482","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0024482","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":"conference-paper","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/A5043667154","display_name":"David P. Williamson","orcid":"https://orcid.org/0000-0002-2884-0058"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David P. Williamson","raw_affiliation_strings":["IBM T. J. Watson Research Labs, P. O. Box 218, 10598, Yorktown Heights, NY, USA","IBM T.J. Watson Research Labs#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM T. J. Watson Research Labs, P. O. Box 218, 10598, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]},{"raw_affiliation_string":"IBM T.J. Watson Research Labs#TAB#","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043667154"],"corresponding_institution_ids":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"],"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":0.11402439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9761000275611877,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9761000275611877,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9480999708175659,"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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9053999781608582,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gadget","display_name":"Gadget","score":0.9524519443511963},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6988543272018433},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.6269928812980652},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6111698746681213},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5501164793968201},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5024576187133789},{"id":"https://openalex.org/keywords/hardness-of-approximation","display_name":"Hardness of approximation","score":0.47108399868011475},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4686930179595947},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.46488142013549805},{"id":"https://openalex.org/keywords/maximum-cut","display_name":"Maximum cut","score":0.45104148983955383},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.42632463574409485},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4096665382385254},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38224393129348755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31333625316619873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27267056703567505},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16383829712867737}],"concepts":[{"id":"https://openalex.org/C119770614","wikidata":"https://www.wikidata.org/wiki/Q5516347","display_name":"Gadget","level":2,"score":0.9524519443511963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6988543272018433},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.6269928812980652},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6111698746681213},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5501164793968201},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5024576187133789},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.47108399868011475},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4686930179595947},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.46488142013549805},{"id":"https://openalex.org/C165526019","wikidata":"https://www.wikidata.org/wiki/Q942557","display_name":"Maximum cut","level":3,"score":0.45104148983955383},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.42632463574409485},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4096665382385254},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38224393129348755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31333625316619873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27267056703567505},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16383829712867737},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bfb0024482","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0024482","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3176904788","https://openalex.org/W21597398","https://openalex.org/W4298153058","https://openalex.org/W2408080066","https://openalex.org/W2268872489","https://openalex.org/W1913543287","https://openalex.org/W2014111643","https://openalex.org/W2963044240","https://openalex.org/W2076399409","https://openalex.org/W2102364390"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}