{"id":"https://openalex.org/W3164916608","doi":"https://doi.org/10.1137/19m1237879","title":"Metrical Task Systems on Trees via Mirror Descent and Unfair Gluing","display_name":"Metrical Task Systems on Trees via Mirror Descent and Unfair Gluing","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3164916608","doi":"https://doi.org/10.1137/19m1237879","mag":"3164916608"},"language":"en","primary_location":{"id":"doi:10.1137/19m1237879","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1237879","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1237879","source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1237879","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021842384","display_name":"S\u00e9bastien Bubeck","orcid":"https://orcid.org/0000-0001-9122-4410"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S\u00e9bastien Bubeck","raw_affiliation_strings":["MIT, Cambridge, MA 02139 USA","\\S University of Washington, Seattle, WA 98195 USA","\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA 02139 USA","institution_ids":["https://openalex.org/I4210110987"]},{"raw_affiliation_string":"\\S University of Washington, Seattle, WA 98195 USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059735243","display_name":"Michael B. Cohen","orcid":"https://orcid.org/0000-0002-7388-6936"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael B. Cohen","raw_affiliation_strings":["\\S University of Washington, Seattle, WA 98195 USA","MIT, Cambridge, MA 02139 USA","\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA"],"affiliations":[{"raw_affiliation_string":"\\S University of Washington, Seattle, WA 98195 USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"MIT, Cambridge, MA 02139 USA","institution_ids":["https://openalex.org/I4210110987"]},{"raw_affiliation_string":"\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028879014","display_name":"James R. Lee","orcid":"https://orcid.org/0000-0002-3512-1617"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James R. Lee","raw_affiliation_strings":["MIT, Cambridge, MA 02139 USA","\\S University of Washington, Seattle, WA 98195 USA","\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA 02139 USA","institution_ids":["https://openalex.org/I4210110987"]},{"raw_affiliation_string":"\\S University of Washington, Seattle, WA 98195 USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024980585","display_name":"Yin Tat Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yin Tat Lee","raw_affiliation_strings":["\\S University of Washington, Seattle, WA 98195 USA","\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA","MIT, Cambridge, MA 02139 USA"],"affiliations":[{"raw_affiliation_string":"\\S University of Washington, Seattle, WA 98195 USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"\\dagger Theory Group, Microsoft Research, Redmond, WA 98052 USA","institution_ids":["https://openalex.org/I1290206253"]},{"raw_affiliation_string":"MIT, Cambridge, MA 02139 USA","institution_ids":["https://openalex.org/I4210110987"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021842384"],"corresponding_institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I201448701","https://openalex.org/I4210110987"],"apc_list":null,"apc_paid":null,"fwci":1.4408,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82535655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"50","issue":"3","first_page":"909","last_page":"923"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":1.0,"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":1.0,"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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9968000054359436,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9919999837875366,"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/metric","display_name":"Metric (unit)","score":0.6109321117401123},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.6092835068702698},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.5978736281394958},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5977417826652527},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.496025413274765},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4548646807670593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36448174715042114},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3597038686275482},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33873945474624634},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.23387005925178528},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.17180892825126648},{"id":"https://openalex.org/keywords/operations-management","display_name":"Operations management","score":0.08616149425506592}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6109321117401123},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.6092835068702698},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5978736281394958},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5977417826652527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.496025413274765},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4548646807670593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36448174715042114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3597038686275482},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33873945474624634},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.23387005925178528},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.17180892825126648},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.08616149425506592},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1237879","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1237879","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1237879","source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/19m1237879","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1237879","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1237879","source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.49000000953674316,"display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G1727161092","display_name":null,"funder_award_id":"CCF-1407779","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1906418360","display_name":null,"funder_award_id":"1740551","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2514421424","display_name":null,"funder_award_id":"Award","funder_id":"https://openalex.org/F4320308943","funder_display_name":"Microsoft Research"},{"id":"https://openalex.org/G2798763028","display_name":"CAREER: The Interplay between Combinatorial Optimization and Algorithmic Convex Geometry","funder_award_id":"1749609","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2816039220","display_name":null,"funder_award_id":"1616297","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5775386550","display_name":null,"funder_award_id":"CCF-1616297","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7116278599","display_name":null,"funder_award_id":"CCF-1749609","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G874486094","display_name":null,"funder_award_id":"CCF-1740551","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320308943","display_name":"Microsoft Research","ror":"https://ror.org/00d0nc645"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3164916608.pdf","grobid_xml":"https://content.openalex.org/works/W3164916608.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W585462275","https://openalex.org/W1543614321","https://openalex.org/W1986829372","https://openalex.org/W2007840228","https://openalex.org/W2025874591","https://openalex.org/W2033156334","https://openalex.org/W2062780596","https://openalex.org/W2113184918","https://openalex.org/W2114493937","https://openalex.org/W2114538202","https://openalex.org/W2161029651","https://openalex.org/W2571257893","https://openalex.org/W2963331653","https://openalex.org/W3030774092","https://openalex.org/W3103476680"],"related_works":["https://openalex.org/W2015327483","https://openalex.org/W1678820847","https://openalex.org/W2559216629","https://openalex.org/W2037211941","https://openalex.org/W4298096494","https://openalex.org/W1553684505","https://openalex.org/W2042403445","https://openalex.org/W2725816051","https://openalex.org/W1607707911","https://openalex.org/W2170414352"],"abstract_inverted_index":{"\\bfA":[0],"\\bfb":[1],"\\bfs":[2],"\\bft":[3,7],"\\bfr":[4],"\\bfa":[5],"\\bfc":[6],".":[8],"We":[9],"consider":[10],"metrical":[11,63],"task":[12,64],"systems":[13],"on":[14,27,37,60],"tree":[15],"metrics":[16],"and":[17],"present":[18],"an":[19,68,76,94],"O(depth":[20],"\\times":[21],"log":[22,78,79],"n)competitive":[23],"randomized":[24,99],"algorithm":[25,71,100],"based":[26,59],"the":[28,38,42,56,82],"mirror":[29,52],"descent":[30,53],"framework":[31],"introduced":[32],"in":[33,81],"our":[34],"prior":[35],"work":[36],"k-server":[39],"problem.":[40],"For":[41],"special":[43],"case":[44],"of":[45,84],"hierarchically":[46],"separated":[47],"trees":[48],"(HSTs),":[49],"we":[50],"use":[51],"to":[54],"refine":[55],"standard":[57],"approach":[58],"gluing":[61],"unfair":[62],"systems.":[65],"This":[66],"yields":[67],"O(log":[69],"n)-competitive":[70],"for":[72,101],"HSTs,":[73],"thus":[74],"removing":[75],"extraneous":[77],"n":[80],"bound":[83],"Combined":[85],"with":[86],"well-known":[87],"HST":[88],"embedding":[89],"theorems,":[90],"this":[91],"also":[92],"gives":[93],"O((log":[95],"n)":[96],"2":[97],")-competitive":[98],"every":[102],"n-point":[103],"metric":[104],"space.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}