{"id":"https://openalex.org/W1974848406","doi":"https://doi.org/10.1137/110834810","title":"Efficient Algorithms for Eulerian Extension and Rural Postman","display_name":"Efficient Algorithms for Eulerian Extension and Rural Postman","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1974848406","doi":"https://doi.org/10.1137/110834810","mag":"1974848406"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/110834810","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://fpt.akt.tu-berlin.de/publications/Eulerian_Extension_and_Rural_Postman_SIDMA.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027034693","display_name":"Frederic Dorn","orcid":null},"institutions":[{"id":"https://openalex.org/I173888879","display_name":"SINTEF","ror":"https://ror.org/01f677e56","country_code":"NO","type":"facility","lineage":["https://openalex.org/I173888879"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Frederic Dorn","raw_affiliation_strings":["SINTEF Energy Research, Trondheim, Norway"],"affiliations":[{"raw_affiliation_string":"SINTEF Energy Research, Trondheim, Norway","institution_ids":["https://openalex.org/I173888879"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040313005","display_name":"Hannes Moser","orcid":null},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hannes Moser","raw_affiliation_strings":["Institut f\u00fcr Informatik, Friedrich-Schiller-Universit\u00e4t Jena, Germany."],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Friedrich-Schiller-Universit\u00e4t Jena, Germany.","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033021388","display_name":"Rolf Niedermeier","orcid":"https://orcid.org/0000-0003-1703-1236"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rolf Niedermeier","raw_affiliation_strings":["Institut f\u00fcr Softwaretechnik und Theoretische Informatik, TU Berlin, Germany."],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Softwaretechnik und Theoretische Informatik, TU Berlin, Germany.","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030931327","display_name":"Mathias Weller","orcid":"https://orcid.org/0000-0002-9653-3690"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mathias Weller","raw_affiliation_strings":["Institut f\u00fcr Softwaretechnik und Theoretische Informatik, TU Berlin, Germany."],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Softwaretechnik und Theoretische Informatik, TU Berlin, Germany.","institution_ids":["https://openalex.org/I4577782"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.563,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":32,"citation_normalized_percentile":{"value":0.924063,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":94},"biblio":{"volume":"27","issue":"1","first_page":"75","last_page":"94"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9992,"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":0.9992,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9973,"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"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.996,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/multigraph","display_name":"Multigraph","score":0.8572246},{"id":"https://openalex.org/keywords/feedback-arc-set","display_name":"Feedback arc set","score":0.55583364},{"id":"https://openalex.org/keywords/arc-routing","display_name":"Arc routing","score":0.5113577}],"concepts":[{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.91804105},{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.8572246},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.77899414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.68500775},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6761966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6227033},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.60297495},{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.55583364},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5445242},{"id":"https://openalex.org/C2778536092","wikidata":"https://www.wikidata.org/wiki/Q4785038","display_name":"Arc routing","level":3,"score":0.5113577},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.49133196},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.44458762},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42377913},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4228116},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3729197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34431985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24315438},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.1670911},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.14546424},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.10379699},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08594805},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/110834810","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.6344","pdf_url":"http://fpt.akt.tu-berlin.de/publications/Eulerian_Extension_and_Rural_Postman_SIDMA.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.6344","pdf_url":"http://fpt.akt.tu-berlin.de/publications/Eulerian_Extension_and_Rural_Postman_SIDMA.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":40,"referenced_works":["https://openalex.org/W1488422606","https://openalex.org/W1511638527","https://openalex.org/W1517036688","https://openalex.org/W1527254034","https://openalex.org/W1557310162","https://openalex.org/W1570425181","https://openalex.org/W1586744224","https://openalex.org/W1591506270","https://openalex.org/W1606657688","https://openalex.org/W1635111306","https://openalex.org/W190702523","https://openalex.org/W1977545325","https://openalex.org/W1995988419","https://openalex.org/W2006933117","https://openalex.org/W2008444606","https://openalex.org/W2011039300","https://openalex.org/W2012760542","https://openalex.org/W2034363746","https://openalex.org/W2035543139","https://openalex.org/W2048832818","https://openalex.org/W2055803317","https://openalex.org/W2059615070","https://openalex.org/W2060069351","https://openalex.org/W2062403584","https://openalex.org/W2064284095","https://openalex.org/W2080182237","https://openalex.org/W2083748805","https://openalex.org/W2104894563","https://openalex.org/W2123789618","https://openalex.org/W2126141749","https://openalex.org/W2154257407","https://openalex.org/W2166023017","https://openalex.org/W2247555971","https://openalex.org/W2395287869","https://openalex.org/W24573320","https://openalex.org/W2482720396","https://openalex.org/W2913688336","https://openalex.org/W4285719527","https://openalex.org/W55260560","https://openalex.org/W61956116"],"related_works":["https://openalex.org/W4297817344","https://openalex.org/W4292730466","https://openalex.org/W4288723498","https://openalex.org/W4287028074","https://openalex.org/W3191289342","https://openalex.org/W2603633312","https://openalex.org/W2555805899","https://openalex.org/W2354764436","https://openalex.org/W2350111251","https://openalex.org/W1512669878"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,22,69],"directed":[3,74,123],"Eulerian":[4,16,57,110],"extension":[5,70,111],"problems":[6,25],"is":[7,49,60],"to":[8,38,50,65,82,121],"make":[9],"a":[10,19,73,88],"given":[11],"directed,":[12],"possibly":[13],"arc-weighted,":[14],"(multi-)graph":[15],"by":[17],"adding":[18],"minimum-cost":[20],"set":[21],"arcs.":[23,71],"These":[24],"have":[26],"natural":[27,109],"applications":[28],"in":[29],"scheduling":[30],"and":[31,34,42],"arc":[32],"routing":[33],"are":[35],"closely":[36],"related":[37],"the":[39,53,66,77,93,122],"Chinese":[40],"Postman":[41,44,96],"Rural":[43,95],"problems.":[45],"Our":[46],"main":[47],"result":[48,91],"show":[51],"that":[52],"NP-hard":[54],"Weighted":[55],"Multigraph":[56],"Extension":[58],"problem":[59,97],"fixed-parameter":[61,89],"tractable":[62],"with":[63],"respect":[64],"number":[67],"${k}$":[68],"For":[72],"$n$-vertex":[75],"multigraph,":[76],"corresponding":[78],"running":[79],"time":[80],"amounts":[81],"${\\ensuremath{O(4^{k}\\cdot":[83],"n^3)}}$.":[84],"This":[85],"also":[86],"implies":[87],"tractability":[90],"for":[92,108],"\u201cequivalent\u201d":[94],"parameterized":[98],"above":[99],"guarantee.":[100],"In":[101],"addition,":[102],"we":[103],"present":[104],"several":[105],"polynomial-time":[106],"algorithms":[107],"problems,":[112],"including":[113],"undirected":[114],"variants":[115],"which":[116],"can":[117],"be":[118],"defined":[119],"analogously":[120],"ones.":[124]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1974848406","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3}],"updated_date":"2025-01-19T13:29:55.326930","created_date":"2016-06-24"}