{"id":"https://openalex.org/W4390098115","doi":"https://doi.org/10.1109/focs57990.2023.00139","title":"Covering Planar Metrics (and Beyond): O(1) Trees Suffice","display_name":"Covering Planar Metrics (and Beyond): O(1) Trees Suffice","publication_year":2023,"publication_date":"2023-11-06","ids":{"openalex":"https://openalex.org/W4390098115","doi":"https://doi.org/10.1109/focs57990.2023.00139"},"language":"en","primary_location":{"id":"doi:10.1109/focs57990.2023.00139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs57990.2023.00139","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)","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/A5003923315","display_name":"Hsien-Chih Chang","orcid":"https://orcid.org/0000-0001-6714-7988"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hsien-Chih Chang","raw_affiliation_strings":["Dartmouth College,USA","Dartmouth College, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dartmouth College,USA","institution_ids":["https://openalex.org/I107672454"]},{"raw_affiliation_string":"Dartmouth College, USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067955248","display_name":"Jonathan Conroy","orcid":null},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Conroy","raw_affiliation_strings":["Dartmouth College,USA","Dartmouth College, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dartmouth College,USA","institution_ids":["https://openalex.org/I107672454"]},{"raw_affiliation_string":"Dartmouth College, USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050273950","display_name":"Hung Le","orcid":"https://orcid.org/0000-0001-8223-9944"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hung Le","raw_affiliation_strings":["UMass,Amherst,USA","UMass, Amherst, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UMass,Amherst,USA","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"UMass, Amherst, USA","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054075729","display_name":"Lazar Milenkovi\u0107","orcid":"https://orcid.org/0000-0003-2657-8241"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Lazar Milenkovic","raw_affiliation_strings":["Tel Aviv University,Israel","Tel Aviv University, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel Aviv University,Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084685735","display_name":"Shay Solomon","orcid":"https://orcid.org/0000-0003-2254-5100"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shay Solomon","raw_affiliation_strings":["Tel Aviv University,Israel","Tel Aviv University, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel Aviv University,Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050147589","display_name":"Cuong Than","orcid":"https://orcid.org/0000-0001-7350-331X"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cuong Than","raw_affiliation_strings":["UMass,Amherst,USA","UMass, Amherst, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UMass,Amherst,USA","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"UMass, Amherst, USA","institution_ids":["https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9314,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.797309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"2231","last_page":"2261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9550999999046326,"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/planar","display_name":"Planar","score":0.7085961103439331},{"id":"https://openalex.org/keywords/covering-space","display_name":"Covering space","score":0.6587380766868591},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6470212936401367},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6270807385444641},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6022900342941284},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5484727621078491},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.5454984903335571},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5422433614730835},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.531938374042511},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5257916450500488},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.48485100269317627},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.46946588158607483},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.45154473185539246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4410941004753113},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4326925575733185},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4058557152748108},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25349199771881104},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2266988456249237}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7085961103439331},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.6587380766868591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6470212936401367},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6270807385444641},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6022900342941284},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5484727621078491},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.5454984903335571},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5422433614730835},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.531938374042511},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5257916450500488},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.48485100269317627},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.46946588158607483},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.45154473185539246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4410941004753113},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4326925575733185},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4058557152748108},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25349199771881104},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2266988456249237},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/focs57990.2023.00139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs57990.2023.00139","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W48861618","https://openalex.org/W1970732121","https://openalex.org/W1981859328","https://openalex.org/W2001075173","https://openalex.org/W2004322147","https://openalex.org/W2005580106","https://openalex.org/W2005985615","https://openalex.org/W2010042187","https://openalex.org/W2011999472","https://openalex.org/W2022995240","https://openalex.org/W2034501275","https://openalex.org/W2038643780","https://openalex.org/W2042899161","https://openalex.org/W2045134120","https://openalex.org/W2049413646","https://openalex.org/W2053578961","https://openalex.org/W2057826895","https://openalex.org/W2059694926","https://openalex.org/W2063900329","https://openalex.org/W2072142932","https://openalex.org/W2075022748","https://openalex.org/W2093455937","https://openalex.org/W2093521781","https://openalex.org/W2096304547","https://openalex.org/W2102465486","https://openalex.org/W2114493937","https://openalex.org/W2120424341","https://openalex.org/W2137120608","https://openalex.org/W2149463264","https://openalex.org/W2154833764","https://openalex.org/W2165094933","https://openalex.org/W2167838689","https://openalex.org/W2172213884","https://openalex.org/W2176446742","https://openalex.org/W2484918492","https://openalex.org/W2493557058","https://openalex.org/W2493698126","https://openalex.org/W2551173872","https://openalex.org/W2571257893","https://openalex.org/W2748812071","https://openalex.org/W2903797494","https://openalex.org/W2938191358","https://openalex.org/W2951760736","https://openalex.org/W2952050889","https://openalex.org/W2963873784","https://openalex.org/W3030774092","https://openalex.org/W3098011928","https://openalex.org/W3103394879","https://openalex.org/W3104014862","https://openalex.org/W3127920245","https://openalex.org/W3137290582","https://openalex.org/W3167218181","https://openalex.org/W4206688115","https://openalex.org/W4214935068","https://openalex.org/W4232548171","https://openalex.org/W4237350530","https://openalex.org/W4242591007","https://openalex.org/W4245608944","https://openalex.org/W4254419859","https://openalex.org/W4281675035","https://openalex.org/W4281745168","https://openalex.org/W4285021491","https://openalex.org/W4286500901","https://openalex.org/W4313227179","https://openalex.org/W4376639584","https://openalex.org/W4389615669","https://openalex.org/W6643673115","https://openalex.org/W6651059365","https://openalex.org/W6704291534","https://openalex.org/W6729167663","https://openalex.org/W6773079701"],"related_works":["https://openalex.org/W4294294347","https://openalex.org/W2279239548","https://openalex.org/W115379796","https://openalex.org/W63976795","https://openalex.org/W2404658402","https://openalex.org/W2610298398","https://openalex.org/W4281992692","https://openalex.org/W2105228010","https://openalex.org/W164473625","https://openalex.org/W122023996"],"abstract_inverted_index":{"While":[0],"research":[1],"on":[2],"the":[3,12,29,78,121,129,144,197,209,227,240,248],"geometry":[4],"of":[5,17,28,40,47,56,62,77,124,211,229,243,250,298,315,332],"planar":[6,18,30,34,134,151,172,186,234,244,259,281,316],"graphs":[7,282,317,320],"has":[8,69,111,117],"been":[9,118],"active":[10],"in":[11,67,73,261,280,329],"past":[13],"decades,":[14],"many":[15],"properties":[16],"metrics":[19,35,126,149,187],"remain":[20],"mysterious.":[21],"This":[22,109],"paper":[23],"studies":[24],"a":[25,37,44,48,54,70,95,190,291,310],"fundamental":[26,158],"aspect":[27],"graph":[31],"geometry:":[32],"covering":[33],"by":[36,177,308],"small":[38,322],"collection":[39,55],"simpler":[41,311],"metrics.":[42],"Specifically,":[43,161],"tree":[45,96,201,222,255,267,285,306],"cover":[46,97,256,268,307],"metric":[49,173],"space":[50,93],"$(X,":[51],"\\delta)$":[52],"is":[53,290,297],"trees,":[57],"so":[58],"that":[59,89,164,294],"every":[60],"pair":[61],"points":[63],"u":[64],"and":[65,101,116,150,214,220,312],"v":[66],"X":[68],"low-distortion":[71],"path":[72],"at":[74],"least":[75],"one":[76],"trees.The":[79],"celebrated":[80],"\u201cDumbbell":[81],"Theorem\u201d":[82],"[ADM":[83],"<sup":[84],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[85],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">+</sup>":[86],"95]":[87],"states":[88],"any":[90,105,166,171,233],"low-dimensional":[91],"Euclidean":[92],"admits":[94],"with":[98,180,203,269,321],"$O(1)$":[99,178],"trees":[100,179],"distortion":[102,181,270],"$1+\\varepsilon$,":[103],"for":[104,133,165,185,232,272],"fixed":[106,168],"$\\varepsilon":[107,169],"\\in(0,1)$.":[108],"result":[110,131,184],"found":[112],"numerous":[113],"algorithmic":[114,278],"applications,":[115],"generalized":[119],"to":[120,143,199],"wider":[122],"family":[123],"doubling":[125],"[BFN19].":[127],"Does":[128],"same":[130],"hold":[132],"metrics?":[135],"A":[136],"positive":[137],"answer":[138,156],"would":[139],"add":[140],"another":[141],"evidence":[142],"well-observed":[145],"connection":[146,216],"between":[147,217],"Euclidean/doubling":[148],"metrics.In":[152],"this":[153,157,330],"work,":[154],"we":[155,162,195,207,225,263,295],"question":[159],"affirmatively.":[160],"show":[163],"given":[167],"\\in(0,1)$,":[170],"can":[174],"be":[175],"covered":[176],"$1+\\varepsilon$.":[182],"Our":[183],"follows":[188],"from":[189,283],"rather":[191],"general":[192],"framework:":[193],"First":[194],"reduce":[196],"problem":[198,328],"constructing":[200,309],"covers":[202],"additive":[204,221,323],"distortion.":[205],"Then":[206],"introduce":[208],"notion":[210],"shortcut":[212,218,230],"partition,":[213],"draw":[215],"partition":[219,231],"cover.":[223,286],"Finally":[224],"prove":[226],"existence":[228],"metric,":[235],"using":[236],"new":[237],"insights":[238],"regarding":[239],"grid-like":[241,288],"structure":[242,289],"graphs.":[245],"To":[246],"demonstrate":[247],"power":[249],"our":[251,284],"framework:\u2022We":[252],"establish":[253],"additional":[254],"results":[257],"beyond":[258,305],"metrics;":[260],"particular,":[262],"present":[264],"an":[265,326],"$O(1)$-size":[266],"$1+\\varepsilon$":[271],"bounded":[273],"treewidth":[274],"metrics;\u2022We":[275],"obtain":[276],"several":[277],"applications":[279],"The":[287],"technical":[292],"contribution":[293],"believe":[296],"independent":[299],"interest.":[300],"We":[301],"showcase":[302],"its":[303],"applicability":[304],"better":[313],"embedding":[314],"into":[318],"$O(1)$-treewidth":[319],"distortion,":[324],"resolving":[325],"open":[327],"line":[331],"research.":[333]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}