{"id":"https://openalex.org/W4404450444","doi":"https://doi.org/10.4230/lipics.socg.2026.3","title":"Lower Bounding the Gromov--Hausdorff distance in Metric Graphs","display_name":"Lower Bounding the Gromov--Hausdorff distance in Metric Graphs","publication_year":2024,"publication_date":"2024-11-14","ids":{"openalex":"https://openalex.org/W4404450444","doi":"https://doi.org/10.4230/lipics.socg.2026.3"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2411.09182","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2411.09182","pdf_url":"https://arxiv.org/pdf/2411.09182","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2411.09182","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066051969","display_name":"Henry Adams","orcid":"https://orcid.org/0000-0002-8103-4135"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adams, Henry","raw_affiliation_strings":["University of Florida, Gainesville, FL, USA"],"raw_orcid":"https://orcid.org/0000-0003-0914-6316","affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021160042","display_name":"Sushovan Majhi","orcid":"https://orcid.org/0000-0001-8689-4321"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Majhi, Sushovan","raw_affiliation_strings":["George Washington University, Washington, DC, USA"],"raw_orcid":"https://orcid.org/0000-0001-8689-4321","affiliations":[{"raw_affiliation_string":"George Washington University, Washington, DC, USA","institution_ids":["https://openalex.org/I193531525"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065552459","display_name":"Fedor Manin","orcid":"https://orcid.org/0000-0002-4545-6998"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Manin, Fedor","raw_affiliation_strings":["University of Toronto, Canada"],"raw_orcid":"https://orcid.org/0000-0002-4545-6998","affiliations":[{"raw_affiliation_string":"University of Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063657601","display_name":"\u017diga Virk","orcid":"https://orcid.org/0000-0001-9016-011X"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Virk, \u017diga","raw_affiliation_strings":["University of Ljubljana, Slovenia","Institute IMFM, Ljubljana, Slovenia"],"raw_orcid":"https://orcid.org/0000-0001-9016-011X","affiliations":[{"raw_affiliation_string":"University of Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"Institute IMFM, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005695480","display_name":"Nicol\u00f2 Zava","orcid":"https://orcid.org/0000-0001-8686-1888"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Zava, Nicol\u00f2","raw_affiliation_strings":["Institute of Science and Technology, Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0001-8686-1888","affiliations":[{"raw_affiliation_string":"Institute of Science and Technology, Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9969000220298767,"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":0.9969000220298767,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9950000047683716,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/hausdorff-distance","display_name":"Hausdorff distance","score":0.7438929080963135},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7010815143585205},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.542794406414032},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5346362590789795},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46110397577285767},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3075298070907593},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.14039167761802673},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11851227283477783},{"id":"https://openalex.org/keywords/marketing","display_name":"Marketing","score":0.05957067012786865}],"concepts":[{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.7438929080963135},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7010815143585205},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.542794406414032},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5346362590789795},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46110397577285767},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3075298070907593},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.14039167761802673},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11851227283477783},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.05957067012786865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2411.09182","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2411.09182","pdf_url":"https://arxiv.org/pdf/2411.09182","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:25809","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.3","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.3/LIPIcs.SoCG.2026.3.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"doi:10.48550/arxiv.2411.09182","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2411.09182","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.4230/lipics.socg.2026.3","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.3","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2411.09182","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2411.09182","pdf_url":"https://arxiv.org/pdf/2411.09182","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Let":[0],"$G$":[1],"be":[2,12],"a":[3,13,45,86,93],"finite,":[4],"connected":[5],"metric":[6,36],"graph":[7,37],"and":[8,61],"let":[9],"$X\\subseteq":[10],"G$":[11],"subset.":[14],"If":[15],"$X$":[16],"is":[17,38,69],"sufficiently":[18],"dense":[19],"in":[20],"$G$,":[21],"we":[22,63],"show":[23,64],"that":[24,65],"the":[25,29,35,39,49,66,70,76,81,90,106],"Gromov--Hausdorff":[26,77],"distance":[27,78,83],"matches":[28],"Hausdorff":[30,82],"distance,":[31],"namely":[32],"$d_\\gh(G,X)=d_\\h(G,X)$.":[33],"When":[34],"circle":[40],"$G=S^1$":[41],"with":[42,101],"circumference":[43],"$2\u03c0$,":[44],"recent":[46],"study":[47],"established":[48],"equality":[50],"$d_\\gh(S^1,X)=d_\\h(S^1,X)$":[51],"whenever":[52],"$d_\\gh(S^1,X)<\\frac\u03c0{6}$.":[53],"Our":[54],"results":[55],"relax":[56],"this":[57],"hypothesis":[58],"to":[59],"$d_\\gh(S^1,X)<\\frac\u03c0{3}$,":[60],"furthermore,":[62],"constant":[67],"$\\frac\u03c0{3}$":[68],"best":[71],"possible.":[72],"We":[73],"lower":[74],"bound":[75],"$d_\\gh(G,X)$":[79],"by":[80],"$d_\\h(G,X)$":[84],"via":[85],"simple":[87],"topological":[88],"obstruction:":[89],"existence":[91],"of":[92,108],"possibly":[94],"discontinuous":[95],"function":[96],"$f\\colon":[97],"G":[98],"\\to":[99],"X$":[100],"too":[102],"small":[103],"distortion":[104],"contradicts":[105],"connectedness":[107],"$G$.":[109]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2024-11-17T00:00:00"}