{"id":"https://openalex.org/W7162513310","doi":"https://doi.org/10.4230/lipics.socg.2026.7","title":"Computing L_\u221e Hausdorff Distances Under Translations: The Interplay of Dimensionality, Symmetry and Discreteness","display_name":"Computing L_\u221e Hausdorff Distances Under Translations: The Interplay of Dimensionality, Symmetry and Discreteness","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162513310","doi":"https://doi.org/10.4230/lipics.socg.2026.7"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25813","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.7","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.7/LIPIcs.SoCG.2026.7.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":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.7/LIPIcs.SoCG.2026.7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128703403","display_name":"Sebastian Angrick","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Angrick, Sebastian","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":"https://orcid.org/0009-0007-9840-9611","affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077490455","display_name":"Kevin Buchin","orcid":"https://orcid.org/0000-0002-3022-7877"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Buchin, Kevin","raw_affiliation_strings":["TU Dortmund, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3022-7877","affiliations":[{"raw_affiliation_string":"TU Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137104694","display_name":"Geri Gokaj","orcid":"https://orcid.org/0009-0002-7500-6848"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gokaj, Geri","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":"https://orcid.org/0009-0002-7500-6848","affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088790846","display_name":"Marvin K\u00fcnnemann","orcid":"https://orcid.org/0000-0003-4813-4852"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"K\u00fcnnemann, Marvin","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4813-4852","affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.85946679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.5056999921798706,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.5056999921798706,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.11230000108480453,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.07129999995231628,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/hausdorff-distance","display_name":"Hausdorff distance","score":0.6680999994277954},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.6525999903678894},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5774000287055969},{"id":"https://openalex.org/keywords/closeness","display_name":"Closeness","score":0.49140000343322754},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.4844000041484833},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.4327000081539154},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4323999881744385},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.43220001459121704},{"id":"https://openalex.org/keywords/outer-measure","display_name":"Outer measure","score":0.4228000044822693}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7990000247955322},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.6680999994277954},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.6525999903678894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6358000040054321},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5774000287055969},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5063999891281128},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.49140000343322754},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.4844000041484833},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.4327000081539154},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C143924541","wikidata":"https://www.wikidata.org/wiki/Q258374","display_name":"Outer measure","level":5,"score":0.4228000044822693},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4138000011444092},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.36390000581741333},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.3070000112056732},{"id":"https://openalex.org/C84496893","wikidata":"https://www.wikidata.org/wiki/Q1135782","display_name":"Urysohn and completely Hausdorff spaces","level":4,"score":0.30329999327659607},{"id":"https://openalex.org/C2779341405","wikidata":"https://www.wikidata.org/wiki/Q1456811","display_name":"Kolmogorov complexity","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2745000123977661},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2639000117778778}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25813","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.7","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.7/LIPIcs.SoCG.2026.7.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":"publishedVersion"},{"id":"doi:10.4230/lipics.socg.2026.7","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.7","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25813","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.7","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.7/LIPIcs.SoCG.2026.7.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":"publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162513310.pdf","grobid_xml":"https://content.openalex.org/works/W7162513310.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"To":[0],"measure":[1],"the":[2,5,46,50,67,71,100,113,120,130,135,138,145,161,165,215,272,293,302,319,332,341,358,385,392,423],"similarity":[3],"of":[4,7,19,36,48,58,90,115,122,148,160,304,365,381,416,426],"shape":[6],"point":[8,34],"sets,":[9],"rather":[10],"than":[11],"their":[12],"mere":[13],"closeness":[14],"in":[15,42,126,171,247,280,316,324,347,375,390,403,421],"space,":[16],"various":[17],"notions":[18],"a":[20,86,181,222,312,363,373,377,396],"Hausdorff":[21,68,104,168,428],"distance":[22,52,69,105],"under":[23,70,384,401,430],"translation":[24],"have":[25],"been":[26],"investigated.":[27],"Specifically,":[28,315],"let":[29],"P":[30],"and":[31,38,125,142,144,191,230,256,265,274,295,351,419],"Q":[32],"denote":[33],"sets":[35],"n":[37,141,217,231,255],"m":[39,202],"points,":[40],"respectively,":[41],"\u211d^d.":[43],"We":[44,109,234,269,355],"consider":[45],"task":[47],"computing":[49,427],"minimum":[51],"d(P,Q+\u03c4)":[53],"over":[54],"an":[55,172,413],"admissible":[56],"set":[57,89],"translations":[59],"\u03c4":[60],"\u2208":[61],"T,":[62],"where":[63],"d(\u22c5,":[64,107],"\u22c5)":[65],"denotes":[66],"L_\u221e-norm.":[72],"As":[73,150],"variants,":[74,124],"we":[75,154,205,310,329],"distinguish":[76],"between":[77,140],"continuous":[78,166,393],"(T":[79,84],"=":[80,228,232,263,306,405],"\u211d^d)":[81],"or":[82,97,102],"discrete":[83,359],"is":[85,129,277,301],"given":[87],"finite":[88],"t":[91],"translations)":[92],"as":[93,95,338,340],"well":[94],"directed":[96,101,167,273,294,333],"undirected":[98,103,275,296,320],"(choosing":[99],"for":[106,186,198,214,226,243,253,261,286,291,308,367],"\u22c5)).":[108],"seek":[110],"to":[111,118,194,318,362],"apply":[112],"paradigm":[114],"fine-grained":[116,424],"complexity":[117,121,425],"understand":[119],"these":[123,382],"particular:":[127,248],"How":[128],"running":[131],"time":[132,175,326],"influenced":[133],"by":[134,220],"dimension":[136],"d,":[137],"relationship":[139],"m,":[143,219],"specific":[146],"choice":[147],"variant?":[149],"our":[151,283],"main":[152],"results,":[153],"obtain:":[155],"-":[156,251,259,268,354],"The":[157],"asymmetric":[158,174],"definition":[159],"most":[162],"studied":[163],"variant,":[164],"distance,":[169],"results":[170,411],"intrinsically":[173],"complexity:":[176],"While":[177],"(Chan,":[178],"SoCG'23)":[179],"established":[180],"symmetric":[182],"O\u0303((nm)^{d/2})":[183],"upper":[184],"bound":[185,210,380,400],"all":[187,282],"d":[188,227,244,262,287,305,368,404],"\u2265":[189,245,288],"3":[190,229,264,289],"proved":[192],"it":[193],"be":[195],"conditionally":[196],"optimal":[197],"combinatorial":[199],"algorithms":[200],"whenever":[201],"\u2264":[203,369],"n,":[204],"show":[206,330,356],"that":[207,271,331,357],"this":[208],"lower":[209,241,284,379,399],"does":[211],"not":[212],"hold":[213,290],"case":[216,276,303],"\u226a":[218],"providing":[221],"combinatorial,":[223],"almost-linear-time":[224],"algorithm":[225],"m^{o(1)}.":[233],"further":[235],"prove":[236],"general,":[237],"i.e.,":[238],"non-combinatorial,":[239],"conditional":[240,313,398],"bounds":[242,285],"3,":[246],"(1)":[249],"m^{\u230ad/2\u230b":[250],"o(1)}":[252,260],"small":[254,266],"(2)":[257],"n^{d/2":[258],"m.":[267],"observe":[270],"closely":[278],"related,":[279],"particular,":[281],"both":[292],"variant.":[297],"A":[298],"remarkable":[299],"exception":[300],"1":[307],"which":[309],"provide":[311],"separation.":[314],"contrast":[317],"variants":[321,334,360,383,394],"being":[322],"solvable":[323],"near-linear":[325],"(Rote,":[327],"IPL'91),":[328],"are":[335],"at":[336],"least":[337],"hard":[339],"additive":[342],"problem":[343],"MaxConv":[344],"LowerBound":[345],"introduced":[346],"(Cygan,":[348],"Mucha,":[349],"Wegrzycki":[350],"Wlodarczyk,":[352],"TALG'19).":[353],"reduce":[361],"variant":[364],"3SUM":[366],"3.":[370],"This":[371],"gives":[372],"barrier":[374],"proving":[376],"tight":[378,397],"Orthogonal":[386],"Vectors":[387],"Hypothesis":[388],"(OVH);":[389],"contrast,":[391],"admit":[395],"OVH":[402],"2":[406],"(Bringmann,":[407],"Nusser,":[408],"JoCG'21).":[409],"These":[410],"reveal":[412],"intricate":[414],"interplay":[415],"dimensionality,":[417],"symmetry":[418],"discreteness":[420],"determining":[422],"distances":[429],"translation.":[431]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-28T00:00:00"}
