{"id":"https://openalex.org/W2952768305","doi":"https://doi.org/10.1137/16m1067196","title":"A $(1+\\varepsilon)$-Embedding of Low Highway Dimension Graphs into Bounded Treewidth Graphs","display_name":"A $(1+\\varepsilon)$-Embedding of Low Highway Dimension Graphs into Bounded Treewidth Graphs","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2952768305","doi":"https://doi.org/10.1137/16m1067196","mag":"2952768305"},"language":"en","primary_location":{"id":"doi:10.1137/16m1067196","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1067196","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1502.04588","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000019988","display_name":"Andreas Emil Feldmann","orcid":"https://orcid.org/0000-0001-6229-5332"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Andreas Emil Feldmann","raw_affiliation_strings":["KAM, Charles University, Prague CZ,"],"affiliations":[{"raw_affiliation_string":"KAM, Charles University, Prague CZ,","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109428407","display_name":"Wai Shing Fung","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089412","display_name":"Applied Optimization (United States)","ror":"https://ror.org/004b0n253","country_code":"US","type":"company","lineage":["https://openalex.org/I4210089412"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wai Shing Fung","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, CA,"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, CA,","institution_ids":["https://openalex.org/I4210089412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111545821","display_name":"Jochen K\u00f6nemann","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089412","display_name":"Applied Optimization (United States)","ror":"https://ror.org/004b0n253","country_code":"US","type":"company","lineage":["https://openalex.org/I4210089412"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jochen K\u00f6nemann","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, CA,"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, CA,","institution_ids":["https://openalex.org/I4210089412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110288840","display_name":"Ian Post","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089412","display_name":"Applied Optimization (United States)","ror":"https://ror.org/004b0n253","country_code":"US","type":"company","lineage":["https://openalex.org/I4210089412"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ian Post","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, CA,"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, CA,","institution_ids":["https://openalex.org/I4210089412"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000019988"],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":null,"apc_paid":null,"fwci":2.3503,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90381289,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"47","issue":"4","first_page":"1667","last_page":"1704"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9983999729156494,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9979000091552734,"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/treewidth","display_name":"Treewidth","score":0.8969675898551941},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7197837233543396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6517133712768555},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5986318588256836},{"id":"https://openalex.org/keywords/metric-dimension","display_name":"Metric dimension","score":0.5697039365768433},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5473946332931519},{"id":"https://openalex.org/keywords/tree-decomposition","display_name":"Tree decomposition","score":0.5341201424598694},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5145763754844666},{"id":"https://openalex.org/keywords/partial-k-tree","display_name":"Partial k-tree","score":0.48260438442230225},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.45482754707336426},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.44650885462760925},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4389822483062744},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4261191487312317},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.406134694814682},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3723061680793762},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2196924090385437},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2065708041191101}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.8969675898551941},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7197837233543396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6517133712768555},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5986318588256836},{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.5697039365768433},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5473946332931519},{"id":"https://openalex.org/C70501317","wikidata":"https://www.wikidata.org/wiki/Q462095","display_name":"Tree decomposition","level":5,"score":0.5341201424598694},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5145763754844666},{"id":"https://openalex.org/C128764233","wikidata":"https://www.wikidata.org/wiki/Q7140374","display_name":"Partial k-tree","level":5,"score":0.48260438442230225},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.45482754707336426},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.44650885462760925},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4389822483062744},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4261191487312317},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.406134694814682},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3723061680793762},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2196924090385437},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2065708041191101},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1067196","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1067196","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"},{"id":"pmh:oai:eprints.whiterose.ac.uk:200958","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1502.04588","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.04588","pdf_url":"https://arxiv.org/pdf/1502.04588","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1502.04588","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.04588","pdf_url":"https://arxiv.org/pdf/1502.04588","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5099999904632568}],"awards":[{"id":"https://openalex.org/G5566021001","display_name":null,"funder_award_id":"P202/12/G061","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W83908813","https://openalex.org/W85521454","https://openalex.org/W656060844","https://openalex.org/W1519520700","https://openalex.org/W1520111182","https://openalex.org/W1521148214","https://openalex.org/W1528485123","https://openalex.org/W1683389017","https://openalex.org/W1715975119","https://openalex.org/W1973529814","https://openalex.org/W1977541023","https://openalex.org/W1986948282","https://openalex.org/W1992380975","https://openalex.org/W1994248285","https://openalex.org/W1995473411","https://openalex.org/W2028047126","https://openalex.org/W2029448190","https://openalex.org/W2041172083","https://openalex.org/W2041571997","https://openalex.org/W2052844078","https://openalex.org/W2053578961","https://openalex.org/W2067512967","https://openalex.org/W2071247529","https://openalex.org/W2082176459","https://openalex.org/W2082353536","https://openalex.org/W2097307233","https://openalex.org/W2098322943","https://openalex.org/W2101622070","https://openalex.org/W2114493937","https://openalex.org/W2127248062","https://openalex.org/W2132169470","https://openalex.org/W2165142526","https://openalex.org/W2293564405","https://openalex.org/W2461311369","https://openalex.org/W2579664199","https://openalex.org/W2611804663","https://openalex.org/W2964124596","https://openalex.org/W4243637616"],"related_works":["https://openalex.org/W2091382007","https://openalex.org/W1485639265","https://openalex.org/W2143406303","https://openalex.org/W2092119436","https://openalex.org/W4309067788","https://openalex.org/W2223243427","https://openalex.org/W143512583","https://openalex.org/W4385772980","https://openalex.org/W2949940357","https://openalex.org/W4226048698"],"abstract_inverted_index":{"Graphs":[0],"with":[1,39],"bounded":[2,36,143],"highway":[3,52,124,170],"dimension":[4,125,140,171],"were":[5],"introduced":[6],"by":[7,71],"Abraham":[8],"et":[9],"al.":[10],"[Proceedings":[11,130],"of":[12,20,50,69,88,101,131,137,168,188],"SODA":[13],"2010,":[14],"pp.":[15,134],"782--793]":[16],"as":[17],"a":[18,33,46,60,74,99],"model":[19],"transportation":[21,108],"networks.":[22],"We":[23,153],"show":[24,55],"that":[25,64,104,176],"any":[26],"such":[27],"graph":[28,48,62],"can":[29],"be":[30],"embedded":[31],"into":[32,142],"distribution":[34],"over":[35],"treewidth":[37,81,144],"graphs":[38,126],"arbitrarily":[40],"small":[41],"distortion.":[42],"More":[43],"concretely,":[44],"given":[45],"weighted":[47,61],"$G=(V,E)$":[49],"constant":[51],"dimension,":[53],"we":[54,127,174],"how":[56],"to":[57,158],"randomly":[58],"compute":[59],"$H=(V,E')$":[63],"distorts":[65],"shortest":[66],"path":[67],"distances":[68],"$G$":[70],"at":[72],"most":[73],"$1+\\varepsilon$":[75],"factor":[76],"in":[77,84,107,162],"expectation,":[78],"and":[79,115,161],"whose":[80],"is":[82],"polylogarithmic":[83],"the":[85,166,177,186],"aspect":[86],"ratio":[87],"$G$.":[89],"Our":[90],"probabilistic":[91],"embedding":[92,121,136],"implies":[93],"quasi-polynomial":[94],"time":[95],"approximation":[96],"schemes":[97],"for":[98,122,150,181],"number":[100],"optimization":[102],"problems":[103],"naturally":[105],"arise":[106],"networks,":[109],"including":[110],"Travelling":[111],"Salesman,":[112],"Steiner":[113],"Tree,":[114],"Facility":[116],"Location.":[117],"To":[118],"construct":[119],"our":[120],"low":[123,138,169,189],"extend":[128],"Talwar's":[129,159],"STOC":[132],"2004,":[133],"281--290]":[135],"doubling":[139,190],"metrics":[141,183],"graphs,":[145],"which":[146],"generalizes":[147],"known":[148],"results":[149],"Euclidean":[151,182],"metrics.":[152,191],"add":[154],"several":[155],"nontrivial":[156],"ingredients":[157],"techniques,":[160],"particular":[163],"thoroughly":[164],"analyze":[165],"structure":[167],"graphs.":[172],"Thus":[173],"demonstrate":[175],"geometric":[178],"toolkit":[179],"used":[180],"extends":[184],"beyond":[185],"class":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2019-06-27T00:00:00"}