{"id":"https://openalex.org/W2748812071","doi":"https://doi.org/10.1137/19m1296021","title":"Metric Embedding via Shortest Path Decompositions","display_name":"Metric Embedding via Shortest Path Decompositions","publication_year":2022,"publication_date":"2022-04-01","ids":{"openalex":"https://openalex.org/W2748812071","doi":"https://doi.org/10.1137/19m1296021","mag":"2748812071"},"language":"en","primary_location":{"id":"doi:10.1137/19m1296021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296021","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078682514","display_name":"Ittai Abraham","orcid":"https://orcid.org/0000-0001-9568-7674"},"institutions":[{"id":"https://openalex.org/I74786994","display_name":"Kitware (United States)","ror":"https://ror.org/02s2acn37","country_code":"US","type":"company","lineage":["https://openalex.org/I74786994"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ittai Abraham","raw_affiliation_strings":["VMWare"],"affiliations":[{"raw_affiliation_string":"VMWare","institution_ids":["https://openalex.org/I74786994"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044890369","display_name":"Arnold Filtser","orcid":"https://orcid.org/0000-0001-9578-9304"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Arnold Filtser","raw_affiliation_strings":["Bar-Ilan University"],"affiliations":[{"raw_affiliation_string":"Bar-Ilan University","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078381067","display_name":"Anupam Gupta","orcid":"https://orcid.org/0000-0001-5579-3405"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anupam Gupta","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066182501","display_name":"Ofer Neiman","orcid":"https://orcid.org/0000-0003-4179-4364"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ofer Neiman","raw_affiliation_strings":["Ben-Gurion University of the Negev"],"affiliations":[{"raw_affiliation_string":"Ben-Gurion University of the Negev","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078682514"],"corresponding_institution_ids":["https://openalex.org/I74786994"],"apc_list":null,"apc_paid":null,"fwci":0.4526,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62620935,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"51","issue":"2","first_page":"290","last_page":"314"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10374","display_name":"Advanced Graph Theory Research","score":0.9986000061035156,"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":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7827550768852234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7763253450393677},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.6425277590751648},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.617357611656189},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5976188778877258},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.5967241525650024},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5274375081062317},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5239615440368652},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.459147185087204},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3833015263080597},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14634117484092712},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08335137367248535}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7827550768852234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7763253450393677},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.6425277590751648},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.617357611656189},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5976188778877258},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.5967241525650024},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5274375081062317},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5239615440368652},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.459147185087204},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3833015263080597},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14634117484092712},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08335137367248535},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1296021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296021","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1453775189","display_name":null,"funder_award_id":"2015813","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1784749800","display_name":null,"funder_award_id":"CCF-1540541","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2336941522","display_name":null,"funder_award_id":"1817/17","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G2564752090","display_name":"CCF-BSF: AF: Small: Metric Embeddings and Partitioning for Minor-Closed Graph Families","funder_award_id":"1617790","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3081260677","display_name":null,"funder_award_id":"CCF-1536002","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5049668581","display_name":null,"funder_award_id":"CCF-1617790","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5552157593","display_name":"AitF: FULL: Collaborative Research:  Practical Foundations for Software-Defined Network Optimization","funder_award_id":"1536002","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6692808261","display_name":null,"funder_award_id":"2015813","funder_id":"https://openalex.org/F4320308960","funder_display_name":"United States - Israel Binational Science Foundation"},{"id":"https://openalex.org/G7315415636","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7334382270","display_name":"BSF: 2014414: New Challenges and Perspectives in Online Algorithms","funder_award_id":"1540541","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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/F4320308960","display_name":"United States - Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W48861618","https://openalex.org/W100489996","https://openalex.org/W1595546089","https://openalex.org/W1902724346","https://openalex.org/W1968429800","https://openalex.org/W1981853164","https://openalex.org/W2001075173","https://openalex.org/W2004322147","https://openalex.org/W2011538048","https://openalex.org/W2012737834","https://openalex.org/W2015577846","https://openalex.org/W2015706743","https://openalex.org/W2017427469","https://openalex.org/W2017713020","https://openalex.org/W2027018686","https://openalex.org/W2032684479","https://openalex.org/W2041493135","https://openalex.org/W2049413646","https://openalex.org/W2054974227","https://openalex.org/W2063491776","https://openalex.org/W2069121074","https://openalex.org/W2075022748","https://openalex.org/W2096304547","https://openalex.org/W2098322943","https://openalex.org/W2098492709","https://openalex.org/W2109300296","https://openalex.org/W2113184918","https://openalex.org/W2125082389","https://openalex.org/W2127248062","https://openalex.org/W2150410057","https://openalex.org/W2151592438","https://openalex.org/W2151633447","https://openalex.org/W2166133603","https://openalex.org/W2176446742","https://openalex.org/W2259676875","https://openalex.org/W2285192099","https://openalex.org/W2583644876","https://openalex.org/W2788840627","https://openalex.org/W2902137312","https://openalex.org/W2944960889","https://openalex.org/W2962980142","https://openalex.org/W2979473749","https://openalex.org/W3098011928"],"related_works":["https://openalex.org/W1511821218","https://openalex.org/W1587078595","https://openalex.org/W2124176527","https://openalex.org/W2985636744","https://openalex.org/W2125058377","https://openalex.org/W2465927132","https://openalex.org/W4387667086","https://openalex.org/W4301463689","https://openalex.org/W2605313623","https://openalex.org/W2133160845"],"abstract_inverted_index":{"We":[0,14],"study":[1],"the":[2,139,160,168,175],"problem":[3],"of":[4,8,24,32,54,70,89,118,143,156,167],"embedding":[5,18,86],"shortest-path":[6],"metrics":[7],"weighted":[9],"graphs":[10,88,124,179,208,214],"into":[11,129,195],"$\\ell_p$":[12,130],"spaces.":[13],"introduce":[15],"a":[16,25,60,67,116,187,216],"new":[17,188,205],"technique":[19],"based":[20],"on":[21],"low-depth":[22],"decompositions":[23],"graph":[26,44,50,169,193],"via":[27],"shortest":[28,33,61],"paths.":[29],"The":[30],"notion":[31],"path":[34,43,62],"decomposition":[35],"(SPD)":[36],"depth":[37,47,55,75,91,182],"is":[38,97,108,165],"inductively":[39],"defined:":[40],"A":[41],"(weighed)":[42],"has":[45,51,73],"SPD":[46,53,74,90,181],"$1$.":[48],"General":[49],"an":[52,84],"$k$":[56,127],"if":[57],"it":[58,107,158],"contains":[59],"whose":[63,71,163],"deletion":[64],"leads":[65],"to":[66,111,185],"graph,":[68],"each":[69],"components":[72],"at":[76,92],"most":[77,93],"$k-1$.":[78],"In":[79],"this":[80,119,136],"paper":[81],"we":[82,121,173],"give":[83,186],"$O(k^{\\min\\{\\nicefrac{1}{p},\\nicefrac{1}{2}\\}})$-distortion":[85],"for":[87,100,105,153,207,213],"$k$.":[94],"This":[95],"result":[96],"asymptotically":[98],"tight":[99,109],"any":[101,191],"fixed":[102,217],"$p>1$,":[103],"while":[104],"$p=1$":[106],"up":[110],"second":[112],"order":[113],"terms.":[114],"As":[115],"corollary":[117],"result,":[120],"show":[122],"that":[123,147,177,190],"having":[125],"pathwidth":[126],"embed":[128],"with":[131,197,209],"distortion":[132,164,198],"$O(k^{\\min\\{\\nicefrac{1}{p},\\nicefrac{1}{2}\\}})$.":[133],"For":[134],"$p=1$,":[135],"improves":[137],"over":[138],"best":[140],"previous":[141],"bound":[142],"Lee":[144],"and":[145,212],"Sidiropoulos":[146],"was":[148],"exponential":[149],"in":[150],"$k$;":[151],"moreover,":[152],"other":[154],"values":[155],"$p$":[157],"gives":[159,204],"first":[161],"embeddings":[162],"independent":[166],"size":[170],"$n$.":[171],"Furthermore,":[172],"use":[174],"fact":[176],"planar":[178,192],"have":[180],"$O(\\log":[183],"n)$":[184],"proof":[189],"embeds":[194],"$\\ell_1$":[196],"$O(\\sqrt{\\log":[199],"n})$.":[200],"Our":[201],"approach":[202],"also":[203],"results":[206],"bounded":[210],"treewidth,":[211],"excluding":[215],"minor.":[218]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}