{"id":"https://openalex.org/W2406829766","doi":"https://doi.org/10.4086/toc.2012.v008a015","title":"","display_name":"","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2406829766","doi":"https://doi.org/10.4086/toc.2012.v008a015","mag":"2406829766"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2012.v008a015","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2012.v008a015","pdf_url":"https://theoryofcomputing.org/articles/v008a015/v008a015.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v008a015/v008a015.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101748190","display_name":"Ashish Goel","orcid":"https://orcid.org/0000-0003-0938-0401"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ashish Goel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110288840","display_name":"Ian Post","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ian Post","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.33954422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"1","first_page":"351","last_page":"368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9955000281333923,"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":0.9955000281333923,"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":0.995199978351593,"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":0.983299970626831,"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/mathematics","display_name":"Mathematics","score":0.6070780158042908},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5643507838249207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5353356599807739},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5285324454307556},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5167362093925476},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.511293888092041},{"id":"https://openalex.org/keywords/concave-function","display_name":"Concave function","score":0.46290266513824463},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4589669704437256},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4319608807563782},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.41381049156188965},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.4113956093788147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39019012451171875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27683427929878235},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2517881989479065}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6070780158042908},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5643507838249207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5353356599807739},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5285324454307556},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5167362093925476},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.511293888092041},{"id":"https://openalex.org/C66690126","wikidata":"https://www.wikidata.org/wiki/Q2914302","display_name":"Concave function","level":3,"score":0.46290266513824463},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4589669704437256},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4319608807563782},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.41381049156188965},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.4113956093788147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39019012451171875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27683427929878235},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2517881989479065},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2012.v008a015","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2012.v008a015","pdf_url":"https://theoryofcomputing.org/articles/v008a015/v008a015.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2012.v008a015","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2012.v008a015","pdf_url":"https://theoryofcomputing.org/articles/v008a015/v008a015.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320307791","display_name":"Cisco Systems","ror":"https://ror.org/03yt1ez60"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2406829766.pdf","grobid_xml":"https://content.openalex.org/works/W2406829766.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1511618541","https://openalex.org/W1531667076","https://openalex.org/W1755312702","https://openalex.org/W1759768216","https://openalex.org/W1786215221","https://openalex.org/W1989669912","https://openalex.org/W1991055327","https://openalex.org/W2018128607","https://openalex.org/W2022174455","https://openalex.org/W2025556735","https://openalex.org/W2041571997","https://openalex.org/W2059707428","https://openalex.org/W2060329104","https://openalex.org/W2075163336","https://openalex.org/W2084224084","https://openalex.org/W2094410510","https://openalex.org/W2096372789","https://openalex.org/W2096881311","https://openalex.org/W2103635929","https://openalex.org/W2106676868","https://openalex.org/W2114393333","https://openalex.org/W2114493937","https://openalex.org/W2124295613","https://openalex.org/W2133156969","https://openalex.org/W2146763892","https://openalex.org/W2147879413","https://openalex.org/W2153992840","https://openalex.org/W2160950139","https://openalex.org/W2169143327","https://openalex.org/W2951475756","https://openalex.org/W3030774092","https://openalex.org/W3137469667","https://openalex.org/W4233380597","https://openalex.org/W4244823362"],"related_works":["https://openalex.org/W2959833232","https://openalex.org/W2949220935","https://openalex.org/W2038387772","https://openalex.org/W2986946279","https://openalex.org/W1990647199","https://openalex.org/W1983162654","https://openalex.org/W2357127731","https://openalex.org/W2363773738","https://openalex.org/W4297582173","https://openalex.org/W1985727224"],"abstract_inverted_index":{"We":[0,11,53],"study":[1],"the":[2,27,77,86,102,109],"single-sink":[3],"buy-at-bulk":[4],"problem":[5],"with":[6],"an":[7,35],"unknown":[8],"cost":[9,28,78,88],"function.":[10,117],"wish":[12],"to":[13,22,39,130],"route":[14],"flow":[15,33],"from":[16],"a":[17,23,55,62,68,83,97,115],"set":[18,63],"of":[19,29,64,85,99,101,133],"demand":[20],"nodes":[21],"root":[24],"node,":[25],"where":[26],"routing":[30],"x":[31],"total":[32],"along":[34],"edge":[36],"is":[37,82,95],"proportional":[38],"f":[40,47,49,76,79,92],"(x)":[41],"for":[42,74,89,114,122],"some":[43],"concave,":[44],"non-decreasing":[45],"function":[46],"satisfying":[48],"(0)":[50],"=":[51],"0.":[52],"present":[54],"simple,":[56],"fast,":[57],"combinatorial":[58],"algorithm":[59],"that":[60,73,90],"takes":[61],"demands":[65],"and":[66],"constructs":[67],"single":[69],"tree":[70,110],"T":[71],"such":[72],"all":[75,123],"(T":[80],")":[81],"47.45approximation":[84],"optimal":[87],"particular":[91],".":[93],"This":[94],"within":[96],"factor":[98],"2.33":[100],"best":[103],"approximation":[104],"ratio":[105],"currently":[106],"achievable":[107],"when":[108],"can":[111],"be":[112],"optimized":[113],"specific":[116],"Trees":[118],"achieving":[119],"simultaneous":[120],"O(1)-approximations":[121],"concave":[124],"functions":[125],"were":[126],"previously":[127],"not":[128],"known":[129],"exist":[131],"regardless":[132],"computation":[134],"time.":[135]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}
