{"id":"https://openalex.org/W1986272823","doi":"https://doi.org/10.1109/focs.2007.52","title":"Minimizing Average Flow-time : Upper and Lower Bounds","display_name":"Minimizing Average Flow-time : Upper and Lower Bounds","publication_year":2007,"publication_date":"2007-10-01","ids":{"openalex":"https://openalex.org/W1986272823","doi":"https://doi.org/10.1109/focs.2007.52","mag":"1986272823"},"language":"en","primary_location":{"id":"doi:10.1109/focs.2007.52","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs.2007.52","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5045952512","display_name":"Naveen Garg","orcid":"https://orcid.org/0000-0001-7923-4464"},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Naveen Garg","raw_affiliation_strings":["Indian Institute of Technology Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029407896","display_name":"Amit Kumar","orcid":"https://orcid.org/0000-0002-3965-6627"},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Amit Kumar","raw_affiliation_strings":["Indian Institute of Technology Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I68891433"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"603","last_page":"613"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9998999834060669,"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"}},{"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/T10374","display_name":"Advanced Graph Theory Research","score":0.998199999332428,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7433838248252869},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7067052125930786},{"id":"https://openalex.org/keywords/competitive-analysis","display_name":"Competitive analysis","score":0.6721845865249634},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6663417816162109},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6580466032028198},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6113903522491455},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6049904823303223},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.5997651219367981},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5610724687576294},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.5307336449623108},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.505035936832428},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.47219714522361755},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.450018048286438},{"id":"https://openalex.org/keywords/online-algorithm","display_name":"Online algorithm","score":0.41720402240753174},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3505483865737915},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3207598030567169},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1915251612663269},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06708928942680359},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06442350149154663},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05677378177642822}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7433838248252869},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7067052125930786},{"id":"https://openalex.org/C102408133","wikidata":"https://www.wikidata.org/wiki/Q5156350","display_name":"Competitive analysis","level":3,"score":0.6721845865249634},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6663417816162109},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6580466032028198},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6113903522491455},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6049904823303223},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.5997651219367981},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5610724687576294},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.5307336449623108},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.505035936832428},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.47219714522361755},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.450018048286438},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.41720402240753174},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3505483865737915},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3207598030567169},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1915251612663269},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06708928942680359},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06442350149154663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05677378177642822},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/focs.2007.52","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs.2007.52","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.129.5077","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.5077","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.iitd.ernet.in/~amitk/focs07.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W36639738","https://openalex.org/W92405270","https://openalex.org/W145900249","https://openalex.org/W1517036688","https://openalex.org/W1559081432","https://openalex.org/W1559482660","https://openalex.org/W1570425181","https://openalex.org/W1607926272","https://openalex.org/W1902951782","https://openalex.org/W1988083342","https://openalex.org/W1994659270","https://openalex.org/W1995725694","https://openalex.org/W2009844010","https://openalex.org/W2047150311","https://openalex.org/W2061513598","https://openalex.org/W2071016718","https://openalex.org/W2072626473","https://openalex.org/W2074109829","https://openalex.org/W2093224650","https://openalex.org/W2102201348","https://openalex.org/W2103811745","https://openalex.org/W2129851433","https://openalex.org/W2150936971","https://openalex.org/W2726059329","https://openalex.org/W2913688336","https://openalex.org/W4243052853"],"related_works":["https://openalex.org/W2012502482","https://openalex.org/W2777672110","https://openalex.org/W2086365412","https://openalex.org/W2949398645","https://openalex.org/W2019137296","https://openalex.org/W2059878569","https://openalex.org/W575343561","https://openalex.org/W2134553994","https://openalex.org/W4310884475","https://openalex.org/W4316652420"],"abstract_inverted_index":{"We":[0,49,78,105],"consider":[1],"the":[2,24,57,68,71,74,100,103,108,112,123,129,134],"problem":[3,113,135],"of":[4,23,31,62,70,102,114],"minimizing":[5,115],"average":[6],"flow":[7,60,116],"time":[8,117],"on":[9,33,99,118,128],"multiple":[10],"machines":[11,35,120],"when":[12],"each":[13],"job":[14],"can":[15,43],"be":[16,137],"assigned":[17],"only":[18],"to":[19,73,90,111,139],"a":[20,28,45],"specified":[21],"subset":[22],"machines.":[25],"This":[26],"is":[27,67],"special":[29],"case":[30],"scheduling":[32],"unrelated":[34],"and":[36,87,121],"we":[37,131],"show":[38,91,132],"that":[39,133],"no":[40],"online":[41],"algorithm":[42,54,61],"have":[44],"bounded":[46],"competitive":[47],"ratio.":[48],"provide":[50],"an":[51,80,92],"O(log":[52],"P)-approximation":[53],"by":[55],"modifying":[56],"single-source":[58],"unsplittable":[59],"Dinitz,":[63],"et.al.":[64],"Here":[65],"P":[66],"ratio":[69],"maximum":[72],"minimum":[75],"processing":[76],"times.":[77],"establish":[79,122],"Omega(log":[81,93],"P)-integrality":[82],"gap":[83],"for":[84],"our":[85],"LP-relaxation":[86],"use":[88],"this":[89],"P/log":[94,142],"log":[95,143],"P)":[96],"lower":[97,126],"bound":[98],"approximability":[101],"problem.":[104],"then":[106],"extend":[107],"hardness":[109],"results":[110],"parallel":[119],"first":[124],"non-trivial":[125],"bounds":[127],"approximability;":[130],"cannot":[136],"approximated":[138],"within":[140],"Omega(radiclog":[141],"P).":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}