{"id":"https://openalex.org/W2230554596","doi":"https://doi.org/10.1007/978-3-642-54862-8_12","title":"Ranking Templates for Linear Loops","display_name":"Ranking Templates for Linear Loops","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2230554596","doi":"https://doi.org/10.1007/978-3-642-54862-8_12","mag":"2230554596"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-54862-8_12","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-54862-8_12","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-54862-8_12.pdf","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":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-54862-8_12.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090592321","display_name":"Jan Leike","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]},{"id":"https://openalex.org/I4210121786","display_name":"Max Planck Institute for Software Systems","ror":"https://ror.org/02pe2kf23","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210121786"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jan Leike","raw_affiliation_strings":["Max Planck Institute for Software Systems, Germany","University of Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Software Systems, Germany","institution_ids":["https://openalex.org/I4210121786"]},{"raw_affiliation_string":"University of Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077581460","display_name":"Matthias Heizmann","orcid":"https://orcid.org/0000-0003-4252-3558"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Heizmann","raw_affiliation_strings":["University of Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"University of Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090592321"],"corresponding_institution_ids":["https://openalex.org/I161046081","https://openalex.org/I4210121786"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":9.5781,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.99057739,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"172","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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/T10639","display_name":"Advanced Software Engineering Methodologies","score":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/template","display_name":"Template","score":0.8471287488937378},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.7571126222610474},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.7342516183853149},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6326026916503906},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5731164216995239},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.517913281917572},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4824255406856537},{"id":"https://openalex.org/keywords/ranking-svm","display_name":"Ranking SVM","score":0.459922194480896},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4523058235645294},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41909387707710266},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3504871726036072},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33224374055862427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30977994203567505},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.204379141330719},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11081477999687195},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09584110975265503}],"concepts":[{"id":"https://openalex.org/C82714645","wikidata":"https://www.wikidata.org/wiki/Q438331","display_name":"Template","level":2,"score":0.8471287488937378},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.7571126222610474},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7342516183853149},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6326026916503906},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5731164216995239},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.517913281917572},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4824255406856537},{"id":"https://openalex.org/C124975894","wikidata":"https://www.wikidata.org/wiki/Q7293290","display_name":"Ranking SVM","level":3,"score":0.459922194480896},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4523058235645294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41909387707710266},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3504871726036072},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33224374055862427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30977994203567505},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.204379141330719},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11081477999687195},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09584110975265503},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-54862-8_12","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-54862-8_12","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-54862-8_12.pdf","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":{"id":"doi:10.1007/978-3-642-54862-8_12","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-54862-8_12","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-54862-8_12.pdf","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3582310573","display_name":null,"funder_award_id":"AVACS","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4064624828","display_name":null,"funder_award_id":"SFB/TR","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4799527623","display_name":null,"funder_award_id":"Transregio","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8203822747","display_name":null,"funder_award_id":"SFB/TR14 AVACS","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2230554596.pdf","grobid_xml":"https://content.openalex.org/works/W2230554596.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1481140196","https://openalex.org/W1482912566","https://openalex.org/W1493060511","https://openalex.org/W1497058589","https://openalex.org/W1505537169","https://openalex.org/W1523037784","https://openalex.org/W1530375435","https://openalex.org/W1542502949","https://openalex.org/W1563374593","https://openalex.org/W1585194019","https://openalex.org/W1589297860","https://openalex.org/W1592840252","https://openalex.org/W1600009974","https://openalex.org/W1608799719","https://openalex.org/W1701051220","https://openalex.org/W1871170357","https://openalex.org/W1963547452","https://openalex.org/W1983764301","https://openalex.org/W1989813138","https://openalex.org/W2039525895","https://openalex.org/W2042108411","https://openalex.org/W2082387287","https://openalex.org/W2096096565","https://openalex.org/W2111366004","https://openalex.org/W2115198108","https://openalex.org/W2122917953","https://openalex.org/W2129883154","https://openalex.org/W2230306527","https://openalex.org/W2293708017","https://openalex.org/W2399439006","https://openalex.org/W2573816347","https://openalex.org/W3041524002","https://openalex.org/W3136358674","https://openalex.org/W4236847445","https://openalex.org/W4237394719","https://openalex.org/W4248689402"],"related_works":["https://openalex.org/W1985455246","https://openalex.org/W1993634787","https://openalex.org/W3125614403","https://openalex.org/W2476923378","https://openalex.org/W2803221307","https://openalex.org/W2951826204","https://openalex.org/W4211001408","https://openalex.org/W2366147410","https://openalex.org/W2983505768","https://openalex.org/W2226076398"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
