{"id":"https://openalex.org/W2009105227","doi":"https://doi.org/10.1137/0404047","title":"Bound Smoothing Under Chirality Constraints","display_name":"Bound Smoothing Under Chirality Constraints","publication_year":1991,"publication_date":"1991-11-01","ids":{"openalex":"https://openalex.org/W2009105227","doi":"https://doi.org/10.1137/0404047","mag":"2009105227"},"language":"en","primary_location":{"id":"doi:10.1137/0404047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0404047","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5111472625","display_name":"Andreas Dress","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andreas W. M. Dress","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084924917","display_name":"Timothy F. Havel","orcid":"https://orcid.org/0000-0001-7939-2091"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Timothy F. Havel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111472625"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6685,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.65796125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"4","issue":"4","first_page":"535","last_page":"549"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9970999956130981,"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":0.9970999956130981,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9948999881744385,"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/mathematics","display_name":"Mathematics","score":0.8309019804000854},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5478212833404541},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4991011619567871},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4755420684814453},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45610031485557556},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.45521682500839233},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4386778771877289},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.42889106273651123},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4180782437324524}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8309019804000854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5478212833404541},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4991011619567871},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4755420684814453},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45610031485557556},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.45521682500839233},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4386778771877289},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.42889106273651123},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4180782437324524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/0404047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0404047","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:hdl:10068/178902","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/178902","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"I - Miscellaneous"},{"id":"pmh:oai:pub.uni-bielefeld.de:1649295","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/1649295","pdf_url":null,"source":{"id":"https://openalex.org/S4306401670","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W560061790","https://openalex.org/W1494380125","https://openalex.org/W1582520000","https://openalex.org/W1963492530","https://openalex.org/W1978730176","https://openalex.org/W1982217069","https://openalex.org/W2010277027","https://openalex.org/W2014447307","https://openalex.org/W2016000144","https://openalex.org/W2036074894","https://openalex.org/W2043691582","https://openalex.org/W2082387287","https://openalex.org/W2090836551","https://openalex.org/W2094338284","https://openalex.org/W2316897621","https://openalex.org/W2511444485","https://openalex.org/W4242602028","https://openalex.org/W4246532761","https://openalex.org/W4250533584","https://openalex.org/W4298290503"],"related_works":["https://openalex.org/W3099445621","https://openalex.org/W2112145019","https://openalex.org/W145900249","https://openalex.org/W2150936971","https://openalex.org/W1573626259","https://openalex.org/W1986272823","https://openalex.org/W2056549194","https://openalex.org/W2139428469","https://openalex.org/W2106097003","https://openalex.org/W2043076786"],"abstract_inverted_index":{"Procedures":[0],"for":[1,81,113,128],"determining":[2],"the":[3,21,45,53,56,59,62,109],"feasibility":[4,46],"of":[5,13,23,26,58,95,108],"lower":[6],"and":[7,116,118],"upper":[8],"bounds":[9],"on":[10],"Euclidean":[11],"distances":[12],"fixed":[14],"dimension":[15],"play":[16],"a":[17,73,124,129],"central":[18],"role":[19],"in":[20,30,48,98,103],"analysis":[22],"many":[24],"kinds":[25],"scientific":[27],"data.":[28],"Shown":[29],"this":[31],"paper":[32],"is":[33,65,69,101],"how":[34],"results":[35,97],"from":[36],"graph":[37],"optimization":[38],"theory":[39,100],"can":[40],"be":[41],"used":[42,70,121],"to":[43,52,71,86,122],"solve":[44],"problem":[47],"one":[49],"dimension,":[50],"subject":[51,85],"condition":[54],"that":[55],"order":[57],"points":[60],"along":[61],"real":[63],"line":[64],"known.":[66],"The":[67,92],"solution":[68],"derive":[72],"PSPACE,":[74],"$O(":[75],"n^{3}\\cdot":[76],"n!":[77],")$-time":[78],"sequential":[79],"algorithm":[80],"finding":[82],"one-dimensional":[83],"representations":[84],"arbitrary":[87],"distance":[88],"(and":[89],"order)":[90],"constraints.":[91],"wider":[93],"applicability":[94],"these":[96],"measurement":[99],"discussed,":[102],"particular,":[104],"Roy\u2019s":[105],"elegant":[106],"proofs":[107],"classical":[110],"representation":[111,126],"theorems":[112],"interval":[114],"orders":[115],"semiorders,":[117],"they":[119],"are":[120],"obtain":[123],"new":[125],"theorem":[127],"ternary":[130],"relation":[131],"called":[132],"$\\varepsilon":[133],"$-collinearity.":[134]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
