{"id":"https://openalex.org/W2057312772","doi":"https://doi.org/10.1007/s10703-006-4341-z","title":"An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps","display_name":"An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2057312772","doi":"https://doi.org/10.1007/s10703-006-4341-z","mag":"2057312772"},"language":"en","primary_location":{"id":"doi:10.1007/s10703-006-4341-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10703-006-4341-z","pdf_url":null,"source":{"id":"https://openalex.org/S3845260","display_name":"Formal Methods in System Design","issn_l":"0925-9856","issn":["0925-9856","1572-8102"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal Methods in System Design","raw_type":"journal-article"},"type":"article","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/A5053520475","display_name":"Roderick Bloem","orcid":"https://orcid.org/0000-0002-1411-5744"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Roderick Bloem","raw_affiliation_strings":["Graz University of Technology, Austria","Graz Univ. of Technology,   Austria"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Graz Univ. of Technology,   Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001013961","display_name":"Harold N. Gabow","orcid":"https://orcid.org/0000-0002-9775-3492"},"institutions":[{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]},{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Harold N. Gabow","raw_affiliation_strings":["University of Colorado, Boulder","University of Colorado \u2010 Boulder"],"affiliations":[{"raw_affiliation_string":"University of Colorado, Boulder","institution_ids":["https://openalex.org/I2802236040","https://openalex.org/I188538660"]},{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077549627","display_name":"Fabio Somenzi","orcid":"https://orcid.org/0000-0002-2085-2003"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fabio Somenzi","raw_affiliation_strings":["University of Colorado, Boulder","University of Colorado \u2010 Boulder"],"affiliations":[{"raw_affiliation_string":"University of Colorado, Boulder","institution_ids":["https://openalex.org/I2802236040","https://openalex.org/I188538660"]},{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053520475"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":{"value":2690,"currency":"EUR","value_usd":3490},"apc_paid":null,"fwci":4.7185,"has_fulltext":false,"cited_by_count":87,"citation_normalized_percentile":{"value":0.95118284,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"1","first_page":"37","last_page":"56"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9987999796867371,"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":0.9987999796867371,"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.690036952495575},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.6102513670921326},{"id":"https://openalex.org/keywords/emptiness","display_name":"Emptiness","score":0.5994336009025574},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5946170091629028},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5485469102859497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.534496009349823},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5180023312568665},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5066846013069153},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4761471748352051},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44638654589653015},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.4141172468662262},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4099445044994354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3431336283683777},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.257607638835907}],"concepts":[{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.690036952495575},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.6102513670921326},{"id":"https://openalex.org/C2779150620","wikidata":"https://www.wikidata.org/wiki/Q1096367","display_name":"Emptiness","level":2,"score":0.5994336009025574},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5946170091629028},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5485469102859497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.534496009349823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5180023312568665},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5066846013069153},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4761471748352051},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44638654589653015},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.4141172468662262},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4099445044994354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3431336283683777},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.257607638835907},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10703-006-4341-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10703-006-4341-z","pdf_url":null,"source":{"id":"https://openalex.org/S3845260","display_name":"Formal Methods in System Design","issn_l":"0925-9856","issn":["0925-9856","1572-8102"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal Methods in System Design","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.167.5150","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.167.5150","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ist.tugraz.at/publications/rbloem/psfiles/FMSD06lockstep.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.302","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://vlsi.colorado.edu/~rbloem/papers/lockstep.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W42134522","https://openalex.org/W1450494211","https://openalex.org/W1503170978","https://openalex.org/W1517566730","https://openalex.org/W1547100201","https://openalex.org/W1548402307","https://openalex.org/W1550083490","https://openalex.org/W1593311747","https://openalex.org/W1605593319","https://openalex.org/W1654252768","https://openalex.org/W1816620374","https://openalex.org/W1964845238","https://openalex.org/W1975657455","https://openalex.org/W1977506662","https://openalex.org/W2020944181","https://openalex.org/W2030624121","https://openalex.org/W2032304805","https://openalex.org/W2080267935","https://openalex.org/W2085849292","https://openalex.org/W2100112273","https://openalex.org/W2103475464","https://openalex.org/W2114817689","https://openalex.org/W2117189826","https://openalex.org/W2118382442","https://openalex.org/W2138856440","https://openalex.org/W2149020136","https://openalex.org/W2913459036","https://openalex.org/W4250266285","https://openalex.org/W4250884204","https://openalex.org/W4251184992","https://openalex.org/W4293278282"],"related_works":["https://openalex.org/W2024521168","https://openalex.org/W2367752232","https://openalex.org/W2946506817","https://openalex.org/W3121073237","https://openalex.org/W4386642012","https://openalex.org/W2904964998","https://openalex.org/W2912897424","https://openalex.org/W4388555903","https://openalex.org/W4255895919","https://openalex.org/W2965171438"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
