{"id":"https://openalex.org/W2003388935","doi":"https://doi.org/10.1145/1978782.1978784","title":"How well can primal-dual and local-ratio algorithms perform?","display_name":"How well can primal-dual and local-ratio algorithms perform?","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2003388935","doi":"https://doi.org/10.1145/1978782.1978784","mag":"2003388935"},"language":"en","primary_location":{"id":"doi:10.1145/1978782.1978784","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1978782.1978784","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/A5109583026","display_name":"Allan Borodin","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Allan Borodin","raw_affiliation_strings":["University of Toronto, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063050661","display_name":"David Cashman","orcid":null},"institutions":[{"id":"https://openalex.org/I22433950","display_name":"Altera (United States)","ror":"https://ror.org/017b7j426","country_code":"US","type":"company","lineage":["https://openalex.org/I22433950"]},{"id":"https://openalex.org/I4210150916","display_name":"Alterra Power (Canada)","ror":"https://ror.org/04kzfav20","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210150916"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"David Cashman","raw_affiliation_strings":["Altera Corporation, Canada","Altera Corporation, Canada#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Altera Corporation, Canada","institution_ids":["https://openalex.org/I4210150916"]},{"raw_affiliation_string":"Altera Corporation, Canada#TAB#","institution_ids":["https://openalex.org/I22433950"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043150610","display_name":"Avner Magen","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Avner Magen","raw_affiliation_strings":["University of Toronto, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109583026"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":0.6522,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68916395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","issue":"3","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T12176","display_name":"Optimization and Packing Problems","score":0.9995999932289124,"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":0.9995999932289124,"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/approximation-algorithm","display_name":"Approximation algorithm","score":0.6008310317993164},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5964570045471191},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5741252303123474},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5019760131835938},{"id":"https://openalex.org/keywords/set-cover-problem","display_name":"Set cover problem","score":0.46647411584854126},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.4467308819293976},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4316387176513672},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4130805730819702},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39641109108924866},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3679977059364319},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3522483706474304},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2670162320137024}],"concepts":[{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6008310317993164},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5964570045471191},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5741252303123474},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5019760131835938},{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.46647411584854126},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.4467308819293976},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4316387176513672},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4130805730819702},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39641109108924866},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3679977059364319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3522483706474304},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2670162320137024},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":5,"locations":[{"id":"doi:10.1145/1978782.1978784","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1978782.1978784","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:CiteSeerX.psu:10.1.1.133.8582","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.133.8582","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ias.edu/csdm/06-07/files/borodin3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.159.1391","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.1391","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~bor/journal-submit20-06-09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.297.7317","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.7317","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~bor/stack-model.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.6638","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.6638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~avner/papers/lower-bounds-stack-model.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W142286274","https://openalex.org/W178169250","https://openalex.org/W1487406052","https://openalex.org/W1512015032","https://openalex.org/W1587123489","https://openalex.org/W1590399153","https://openalex.org/W1607101114","https://openalex.org/W1608651920","https://openalex.org/W1928219016","https://openalex.org/W1965229006","https://openalex.org/W1970290925","https://openalex.org/W1970592111","https://openalex.org/W1972894929","https://openalex.org/W1990313671","https://openalex.org/W1990317614","https://openalex.org/W1990327548","https://openalex.org/W1990800802","https://openalex.org/W1991055327","https://openalex.org/W1991528957","https://openalex.org/W1992649763","https://openalex.org/W1996696855","https://openalex.org/W2001139415","https://openalex.org/W2003159902","https://openalex.org/W2003902046","https://openalex.org/W2005527711","https://openalex.org/W2005960287","https://openalex.org/W2008305525","https://openalex.org/W2011823863","https://openalex.org/W2013652529","https://openalex.org/W2015423869","https://openalex.org/W2023546589","https://openalex.org/W2027515293","https://openalex.org/W2029777782","https://openalex.org/W2031347356","https://openalex.org/W2033267048","https://openalex.org/W2039298646","https://openalex.org/W2064600658","https://openalex.org/W2066408761","https://openalex.org/W2074557115","https://openalex.org/W2083858754","https://openalex.org/W2083896132","https://openalex.org/W2095785938","https://openalex.org/W2098361906","https://openalex.org/W2101017768","https://openalex.org/W2121370879","https://openalex.org/W2130407580","https://openalex.org/W2130640756","https://openalex.org/W2132274124","https://openalex.org/W2136149017","https://openalex.org/W2136382702","https://openalex.org/W2139841919","https://openalex.org/W2143996311","https://openalex.org/W2146823188","https://openalex.org/W2151669659","https://openalex.org/W2159579504","https://openalex.org/W2161836078","https://openalex.org/W2162898372","https://openalex.org/W2169212776","https://openalex.org/W2174864496","https://openalex.org/W2611804663","https://openalex.org/W2914843939","https://openalex.org/W3023912806","https://openalex.org/W3135922541","https://openalex.org/W3136693265","https://openalex.org/W4205264571","https://openalex.org/W4300550233","https://openalex.org/W4389615663","https://openalex.org/W6844382842"],"related_works":["https://openalex.org/W2367195720","https://openalex.org/W1968497507","https://openalex.org/W1998126097","https://openalex.org/W1980288485","https://openalex.org/W2009976792","https://openalex.org/W2004321562","https://openalex.org/W328736688","https://openalex.org/W2995411114","https://openalex.org/W3184075718","https://openalex.org/W2404561224"],"abstract_inverted_index":{"We":[0],"define":[1],"an":[2],"algorithmic":[3],"paradigm,":[4],"the":[5,40,46,51],"stack":[6,22,47],"model,":[7,48],"that":[8],"captures":[9],"many":[10],"primal-dual":[11,58],"and":[12,18,27,32,59,62,80],"local-ratio":[13,60],"algorithms":[14,61],"for":[15,70,76,84],"approximating":[16],"covering":[17],"packing":[19],"problems.":[20],"The":[21],"model":[23],"is":[24],"defined":[25],"syntactically":[26],"without":[28],"any":[29],"complexity":[30],"limitations":[31],"hence":[33],"our":[34],"approximation":[35],"bounds":[36],"are":[37],"independent":[38],"of":[39,53,57],"P":[41],"versus":[42],"NP":[43],"question.":[44],"Using":[45],"we":[49],"bound":[50],"performance":[52],"a":[54,64,73,81],"broad":[55],"class":[56],"supply":[63],"(log":[65],"n":[66],"+1)/2":[67],"inapproximability":[68,75,83],"result":[69],"set":[71],"cover,":[72],"4/3":[74],"min":[77],"Steiner":[78],"tree,":[79],"0.913":[82],"interval":[85],"scheduling":[86],"on":[87],"two":[88],"machines.":[89]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}