{"id":"https://openalex.org/W1556543317","doi":"https://doi.org/10.1145/1361192.1361198","title":"An asymptotic approximation scheme for multigraph edge coloring","display_name":"An asymptotic approximation scheme for multigraph edge coloring","publication_year":2008,"publication_date":"2008-05-01","ids":{"openalex":"https://openalex.org/W1556543317","doi":"https://doi.org/10.1145/1361192.1361198","mag":"1556543317"},"language":"en","primary_location":{"id":"doi:10.1145/1361192.1361198","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1361192.1361198","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5082922326","display_name":"Peter Sanders","orcid":"https://orcid.org/0000-0003-3330-9349"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210119349","display_name":"Karlsruhe University of Education","ror":"https://ror.org/01t1kq612","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210119349"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Sanders","raw_affiliation_strings":["University of Karlsruhe","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Karlsruhe","institution_ids":["https://openalex.org/I4210119349"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089128021","display_name":"David Steurer","orcid":"https://orcid.org/0000-0002-3908-8180"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"David Steurer","raw_affiliation_strings":["Max Planck Institute for Computer Science","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Computer Science","institution_ids":[]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3929,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65079365,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"4","issue":"2","first_page":"1","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9933000206947327,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9933000206947327,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9690999984741211,"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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9527000188827515,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/multigraph","display_name":"Multigraph","score":0.8831921815872192},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.6997206807136536},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6726301908493042},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6559839248657227},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6463062763214111},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.6255735158920288},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.5300611853599548},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.5193025469779968},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5164013504981995},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5020294189453125},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.4561322331428528},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4529435336589813},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.4295574426651001},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41537562012672424},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1624598205089569},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.10072657465934753}],"concepts":[{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.8831921815872192},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.6997206807136536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6726301908493042},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6559839248657227},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6463062763214111},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.6255735158920288},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.5300611853599548},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.5193025469779968},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5164013504981995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5020294189453125},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.4561322331428528},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4529435336589813},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.4295574426651001},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41537562012672424},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1624598205089569},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.10072657465934753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1145/1361192.1361198","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1361192.1361198","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:edoc.mpg.de:279135","is_oa":false,"landing_page_url":"http://edoc.mpg.de/279135","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-05), SIAM, 897-906 (2005)","raw_type":"Conference-Paper"},{"id":"pmh:oai:edoc.mpg.de:279136","is_oa":false,"landing_page_url":"http://edoc.mpg.de/279136","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"16th ACM-SIAM Symposium on Discrete Algorithms, ACM/SIAM, 897-906 (2005)","raw_type":"Conference-Paper"},{"id":"pmh:oai:pure.mpg.de:item_1328789","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-259E-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-05)","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:pure.mpg.de:item_1328790","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-25A0-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"16th ACM-SIAM Symposium on Discrete Algorithms","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"mag:2617183178","is_oa":false,"landing_page_url":"https://www.cs.cornell.edu/~dsteurer/papers/mecp.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306420974","display_name":"Symposium on Discrete Algorithms","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Symposium on Discrete Algorithms","raw_type":null},{"id":"mag:1556543317","is_oa":false,"landing_page_url":"http://pubman.mpdl.mpg.de/pubman/item/escidoc:1328790","pdf_url":null,"source":{"id":"https://openalex.org/S4306533943","display_name":"Untitled Event","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Untitled Event","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G445270546","display_name":null,"funder_award_id":"SA 933/1-2","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1971663478","https://openalex.org/W1980334956","https://openalex.org/W1987475644","https://openalex.org/W2020972089","https://openalex.org/W2042274567","https://openalex.org/W2044004462","https://openalex.org/W2102669784","https://openalex.org/W2140029748","https://openalex.org/W2330003519"],"related_works":["https://openalex.org/W2617183178","https://openalex.org/W1567788322","https://openalex.org/W2099431183","https://openalex.org/W2902629052","https://openalex.org/W2913993818","https://openalex.org/W2345283763","https://openalex.org/W2141026984","https://openalex.org/W2735767732","https://openalex.org/W1592124149","https://openalex.org/W1915011574","https://openalex.org/W387257795","https://openalex.org/W1606240940","https://openalex.org/W1539756146","https://openalex.org/W3037855705","https://openalex.org/W2913012475","https://openalex.org/W1963724232","https://openalex.org/W1709205181","https://openalex.org/W2535994856","https://openalex.org/W2949380505","https://openalex.org/W2785504563"],"abstract_inverted_index":{"The":[0,52],"edge":[1,42,93],"coloring":[2,43],"problem":[3],"considers":[4],"the":[5,26,32,83,88,91],"assignment":[6],"of":[7,13,17,44,68,85,90],"colors":[8,14],"from":[9],"a":[10,18,57,63],"minimum":[11],"number":[12,84],"to":[15,31],"edges":[16,24,49],"graph":[19],"such":[20],"that":[21,46],"no":[22],"two":[23],"with":[25],"same":[27,33],"color":[28],"are":[29,50],"incident":[30],"node.":[34],"We":[35],"give":[36],"polynomial":[37,81],"time":[38,80],"algorithms":[39,55,70],"for":[40],"approximate":[41],"multigraphs,":[45],"is,":[47],"parallel":[48],"allowed.":[51],"best":[53],"previous":[54],"achieve":[56],"fixed":[58],"constant":[59],"approximation":[60],"factor":[61],"plus":[62],"small":[64],"additive":[65],"offset.":[66],"One":[67],"our":[69],"achieves":[71],"solution":[72],"quality":[73],"opt":[74],"+":[75],"\u221a9opt/2":[76],"and":[77,87],"has":[78],"execution":[79],"in":[82],"nodes":[86],"logarithm":[89],"maximum":[92],"multiplicity.":[94]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
