{"id":"https://openalex.org/W2034674913","doi":"https://doi.org/10.1145/1060590.1060676","title":"Balanced metric labeling","display_name":"Balanced metric labeling","publication_year":2005,"publication_date":"2005-05-22","ids":{"openalex":"https://openalex.org/W2034674913","doi":"https://doi.org/10.1145/1060590.1060676","mag":"2034674913"},"language":"en","primary_location":{"id":"doi:10.1145/1060590.1060676","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060590.1060676","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-seventh annual ACM symposium on Theory of computing","raw_type":"proceedings-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/A5025400832","display_name":"Joseph Naor","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Joseph (Seffi) Naor","raw_affiliation_strings":["Technion, Haifa, Israel","Technion , Haifa , Israel"],"affiliations":[{"raw_affiliation_string":"Technion, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Technion , Haifa , Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068494085","display_name":"Roy Schwartz","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Roy Schwartz","raw_affiliation_strings":["Technion, Haifa, Israel","Technion , Haifa , Israel"],"affiliations":[{"raw_affiliation_string":"Technion, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Technion , Haifa , Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025400832"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.3366,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.61432137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"582","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9984999895095825,"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":0.9984999895095825,"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":0.9955000281333923,"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/T12288","display_name":"Optimization and Search Problems","score":0.9950000047683716,"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/randomized-rounding","display_name":"Randomized rounding","score":0.7779293060302734},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.6406226754188538},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6166632771492004},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.5981049537658691},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.570624589920044},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5520673990249634},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5484620928764343},{"id":"https://openalex.org/keywords/triangle-inequality","display_name":"Triangle inequality","score":0.548014760017395},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5388052463531494},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48820286989212036},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4505296051502228},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4360389709472656},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4245378077030182},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3378385901451111},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29399600625038147},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10756951570510864}],"concepts":[{"id":"https://openalex.org/C32029473","wikidata":"https://www.wikidata.org/wiki/Q7292010","display_name":"Randomized rounding","level":3,"score":0.7779293060302734},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.6406226754188538},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6166632771492004},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.5981049537658691},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.570624589920044},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5520673990249634},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5484620928764343},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.548014760017395},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5388052463531494},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48820286989212036},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4505296051502228},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4360389709472656},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4245378077030182},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3378385901451111},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29399600625038147},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10756951570510864},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1060590.1060676","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060590.1060676","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-seventh annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1964669037","https://openalex.org/W1977360022","https://openalex.org/W1981176059","https://openalex.org/W1981676508","https://openalex.org/W2020632401","https://openalex.org/W2023212718","https://openalex.org/W2041571997","https://openalex.org/W2043520568","https://openalex.org/W2048843200","https://openalex.org/W2052844078","https://openalex.org/W2061130579","https://openalex.org/W2062502830","https://openalex.org/W2068871408","https://openalex.org/W2082353536","https://openalex.org/W2107957194","https://openalex.org/W2108426130","https://openalex.org/W2114493937","https://openalex.org/W2129027842","https://openalex.org/W2150148016","https://openalex.org/W2496163386"],"related_works":["https://openalex.org/W1581948717","https://openalex.org/W1916943706","https://openalex.org/W2002272911","https://openalex.org/W2099734427","https://openalex.org/W2051253470","https://openalex.org/W2543175834","https://openalex.org/W276709744","https://openalex.org/W4388968519","https://openalex.org/W4293997817","https://openalex.org/W2163115662"],"abstract_inverted_index":{"We":[0,66,89,236],"define":[1],"the":[2,10,43,69,72,91,137,161,175,195,201,210,220,224,227,239],"balanced":[3,32,51],"metric":[4,11,33,74,185],"labeling":[5,12,34],"problem,":[6,13,98],"a":[7,19,37,147,152,164,183,189,250],"generalization":[8,38],"of":[9,39,45,53,111,139,151,160,197,223,229,241,253,258],"in":[14,42,62,163],"which":[15],"each":[16,133,233,245],"label":[17,134,191,246],"has":[18],"capacity,":[20],"i.e.,":[21],"at":[22,116],"most":[23,117],"l":[24,123,130],"vertices":[25,131,230,242],"can":[26],"be":[27],"assigned":[28,212,231,243],"to":[29,132,213,218,232,244],"it.":[30],"The":[31],"problem":[35],"is":[36,56,75,136,144,200,207,247],"fundamental":[40],"problems":[41],"area":[44],"approximation":[46,94,109,142],"algorithms,":[47],"e.g.,":[48],"arrangements":[49],"and":[50,77,170,188,226],"partitions":[52],"graphs.":[54],"It":[55],"also":[57],"motivated":[58],"by":[59],"resource":[60],"limitations":[61],"certain":[63],"practical":[64],"scenarios.":[65],"focus":[67],"on":[68,146],"case":[70,81],"where":[71],"given":[73],"uniform":[76],"note":[78,237],"that":[79,156,173,203,238],"this":[80,97],"alone":[82],"encompasses":[83],"various":[84],"well-known":[85],"graph":[86,162],"partitioning":[87],"problems.":[88],"present":[90],"first":[92],"(pseudo)":[93],"algorithm":[95,143],"for":[96,100,255],"achieving":[99],"any":[101],"\u03b5,":[102,122],"0":[103],"<":[104,106],"\u03b5":[105],"1,":[107],"an":[108,158],"factor":[110],"O((ln":[112],"n)/\u03b5),":[113],"while":[114],"assigning":[115],"min":[118],"{O(ln":[119],"k)/1":[120],"-":[121],"+":[124,128],"1|":[125],"(":[126],"1":[127],"\u03b5)":[129],"(k":[135],"number":[138,228,240],"labels).":[140],"Our":[141,177],"based":[145],"novel":[148],"randomized":[149,178,184,190],"rounding":[150,179],"linear":[153],"programming":[154],"formulation":[155],"combines":[157],"embedding":[159],"simplex":[165],"together":[166],"with":[167],"spreading":[168],"metrics":[169],"additional":[171],"constraints":[172],"strengthen":[174],"formulation.":[176],"technique":[180,187],"uses":[181],"both":[182],"decomposition":[186],"assignment":[192],"technique.":[193],"At":[194],"heart":[196],"our":[198],"approach":[199],"fact":[202],"only":[204],"limited":[205],"dependency":[206],"created":[208],"between":[209],"labels":[211],"different":[214],"vertices,":[215],"allowing":[216],"us":[217],"bound":[219],"expected":[221],"cost":[222],"solution":[225],"label,":[234],"simultaneously.":[235],"bounded":[248],"via":[249],"new":[251],"inequality":[252],"Janson[15]":[254],"tail":[256],"bounds":[257],"(partly)":[259],"dependent":[260],"random":[261],"variables.":[262]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}