{"id":"https://openalex.org/W1564240183","doi":"https://doi.org/10.1007/978-3-540-25938-1_6","title":"Formal Development and Verification of Approximation Algorithms Using Auxiliary Variables","display_name":"Formal Development and Verification of Approximation Algorithms Using Auxiliary Variables","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1564240183","doi":"https://doi.org/10.1007/978-3-540-25938-1_6","mag":"1564240183"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-25938-1_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-25938-1_6","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/A5042138172","display_name":"Rudolf Berghammer","orcid":null},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Kiel University","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Rudolf Berghammer","raw_affiliation_strings":["Institut f\u00fcr Informatik und Praktische Mathematik, Universit\u00e4t Kiel, Olshausenstra\u00dfe 40, D-24098, Kiel, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik und Praktische Mathematik, Universit\u00e4t Kiel, Olshausenstra\u00dfe 40, D-24098, Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070224469","display_name":"Markus M\u00fcller-Olm","orcid":"https://orcid.org/0009-0001-2229-9651"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus M\u00fcller-Olm","raw_affiliation_strings":["Fachbereich 4, Lehrstuhl V, Universit\u00e4t Dortmund, Baroper Stra\u00dfe 301, D-44221, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich 4, Lehrstuhl V, Universit\u00e4t Dortmund, Baroper Stra\u00dfe 301, D-44221, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042138172"],"corresponding_institution_ids":["https://openalex.org/I32021983"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.12477538,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"59","last_page":"74"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/mathematical-proof","display_name":"Mathematical proof","score":0.7922097444534302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7748301029205322},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.6351895332336426},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5517020225524902},{"id":"https://openalex.org/keywords/formal-methods","display_name":"Formal methods","score":0.44863221049308777},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3659650683403015},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34264370799064636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18179553747177124},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.17511793971061707}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7922097444534302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7748301029205322},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.6351895332336426},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5517020225524902},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.44863221049308777},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3659650683403015},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34264370799064636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18179553747177124},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.17511793971061707},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-25938-1_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-25938-1_6","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1481018260","https://openalex.org/W1543921836","https://openalex.org/W1967175382","https://openalex.org/W1990313671","https://openalex.org/W2003967246","https://openalex.org/W2017216075","https://openalex.org/W2052064586","https://openalex.org/W2069300761","https://openalex.org/W2090309908","https://openalex.org/W2103953153","https://openalex.org/W2111706174","https://openalex.org/W2132750992","https://openalex.org/W2142524717","https://openalex.org/W2147543351","https://openalex.org/W2156461803","https://openalex.org/W2160888386","https://openalex.org/W2378259225","https://openalex.org/W2397784562","https://openalex.org/W2504620871","https://openalex.org/W2752885492","https://openalex.org/W2911952004","https://openalex.org/W2987907651","https://openalex.org/W4210241296"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W1586813864"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}