{"id":"https://openalex.org/W4416021383","doi":"https://doi.org/10.48550/arxiv.2510.14777","title":"A Levelset Algorithm for 3D-Tarski","display_name":"A Levelset Algorithm for 3D-Tarski","publication_year":2025,"publication_date":"2025-10-16","ids":{"openalex":"https://openalex.org/W4416021383","doi":"https://doi.org/10.48550/arxiv.2510.14777"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2510.14777","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.14777","pdf_url":"https://arxiv.org/pdf/2510.14777","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.14777","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019688727","display_name":"Sebastian Haslebacher","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Haslebacher, Sebastian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072039248","display_name":"Jonas F. Lill","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lill, Jonas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019688727"],"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.7231000065803528,"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":0.7231000065803528,"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":0.060499999672174454,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.03420000150799751,"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/function","display_name":"Function (biology)","score":0.49129998683929443},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4821999967098236},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4632999897003174},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4366999864578247},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.38940000534057617},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.3824000060558319},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3571999967098236}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5789999961853027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5685999989509583},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49129998683929443},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4632999897003174},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4366999864578247},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3707999885082245},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3253999948501587},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29280000925064087},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C62469222","wikidata":"https://www.wikidata.org/wiki/Q17092103","display_name":"Hybrid algorithm (constraint satisfaction)","level":5,"score":0.2583000063896179}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.14777","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.14777","pdf_url":"https://arxiv.org/pdf/2510.14777","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},{"id":"doi:10.48550/arxiv.2510.14777","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.14777","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.14777","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.14777","pdf_url":"https://arxiv.org/pdf/2510.14777","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416021383.pdf","grobid_xml":"https://content.openalex.org/works/W4416021383.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,8,13],"simple":[3],"new":[4],"algorithm":[5,22,53],"for":[6],"finding":[7],"Tarski":[9],"fixed":[10],"point":[11],"of":[12],"monotone":[14],"function":[15],"$F":[16],":":[17],"[N]^3":[18],"\\rightarrow":[19],"[N]^3$.":[20],"Our":[21],"runs":[23],"in":[24],"$O(\\log^2":[25,30],"N)$":[26,31,38],"time":[27],"and":[28],"makes":[29],"queries":[32],"to":[33,43,55],"$F$,":[34],"matching":[35],"the":[36,50],"$\u03a9(\\log^2":[37],"query":[39],"lower":[40],"bound":[41],"due":[42,54],"Etessami":[44],"et":[45,57],"al.":[46,58],"as":[47,49],"well":[48],"existing":[51],"state-of-the-art":[52],"Fearnley":[56]},"counts_by_year":[],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-18T00:00:00"}