{"id":"https://openalex.org/W2295465424","doi":"https://doi.org/10.1137/151002666","title":"Exploiting Chordal Structure in Polynomial Ideals: A Gr\u00f6bner Bases Approach","display_name":"Exploiting Chordal Structure in Polynomial Ideals: A Gr\u00f6bner Bases Approach","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2295465424","doi":"https://doi.org/10.1137/151002666","mag":"2295465424"},"language":"en","primary_location":{"id":"doi:10.1137/151002666","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151002666","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1411.1745","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047692253","display_name":"Diego Cifuentes","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Diego Cifuentes","raw_affiliation_strings":["Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge MA 02139, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge MA 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge MA 02139, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge MA 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031935416"],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":5.0577,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.95315959,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"30","issue":"3","first_page":"1534","last_page":"1570"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10142","display_name":"Formal Methods in Verification","score":0.9810000061988831,"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/chordal-graph","display_name":"Chordal graph","score":0.8721317648887634},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.7226569652557373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6739528179168701},{"id":"https://openalex.org/keywords/interval-graph","display_name":"Interval graph","score":0.5203549265861511},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4843910336494446},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48157262802124023},{"id":"https://openalex.org/keywords/partial-k-tree","display_name":"Partial k-tree","score":0.45827198028564453},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42332789301872253},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39273524284362793},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3822166621685028},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.33309805393218994},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.14842408895492554},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1204507052898407}],"concepts":[{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.8721317648887634},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.7226569652557373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6739528179168701},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.5203549265861511},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4843910336494446},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48157262802124023},{"id":"https://openalex.org/C128764233","wikidata":"https://www.wikidata.org/wiki/Q7140374","display_name":"Partial k-tree","level":5,"score":0.45827198028564453},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42332789301872253},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39273524284362793},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3822166621685028},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.33309805393218994},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.14842408895492554},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1204507052898407},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/151002666","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151002666","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:oai:arXiv.org:1411.1745","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.1745","pdf_url":"https://arxiv.org/pdf/1411.1745","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:1411.1745","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.1745","pdf_url":"https://arxiv.org/pdf/1411.1745","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":[],"awards":[{"id":"https://openalex.org/G4095032630","display_name":null,"funder_award_id":"FA9550-11-1-0305","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W16627279","https://openalex.org/W144954708","https://openalex.org/W217710249","https://openalex.org/W1505369303","https://openalex.org/W1514374891","https://openalex.org/W1518341038","https://openalex.org/W1525447969","https://openalex.org/W1565047086","https://openalex.org/W1570420806","https://openalex.org/W1593793857","https://openalex.org/W1985548249","https://openalex.org/W1989923040","https://openalex.org/W1994061162","https://openalex.org/W2008773301","https://openalex.org/W2010865943","https://openalex.org/W2018501141","https://openalex.org/W2021180976","https://openalex.org/W2037106315","https://openalex.org/W2061782500","https://openalex.org/W2063104797","https://openalex.org/W2066130115","https://openalex.org/W2071596701","https://openalex.org/W2073072937","https://openalex.org/W2077870553","https://openalex.org/W2081659888","https://openalex.org/W2085045434","https://openalex.org/W2085482277","https://openalex.org/W2085550081","https://openalex.org/W2086119402","https://openalex.org/W2089328508","https://openalex.org/W2106138233","https://openalex.org/W2113280143","https://openalex.org/W2143474538","https://openalex.org/W2148417962","https://openalex.org/W2153918277","https://openalex.org/W2167797964","https://openalex.org/W2175098281","https://openalex.org/W2175714895","https://openalex.org/W2259690454","https://openalex.org/W2337098149","https://openalex.org/W2400568052","https://openalex.org/W2426452510","https://openalex.org/W3030441687","https://openalex.org/W3098862099","https://openalex.org/W4205509729","https://openalex.org/W4238102028","https://openalex.org/W4248080568","https://openalex.org/W4285719527","https://openalex.org/W4292070118","https://openalex.org/W4298231803","https://openalex.org/W4301786906"],"related_works":["https://openalex.org/W239742334","https://openalex.org/W1987143101","https://openalex.org/W2788975631","https://openalex.org/W2963009577","https://openalex.org/W1480846237","https://openalex.org/W1544821268","https://openalex.org/W1548014395","https://openalex.org/W3037533092","https://openalex.org/W1726008105","https://openalex.org/W4301183116"],"abstract_inverted_index":{"Chordal":[0,164],"structure":[1,33,44,104,165],"and":[2,17,98,186],"bounded":[3],"treewidth":[4,135],"allow":[5],"for":[6,39,148],"efficient":[7,73],"computation":[8],"in":[9,34,54,116,159,167,178],"numerical":[10],"linear":[11,158],"algebra,":[12],"graphical":[13],"models,":[14],"constraint":[15],"satisfaction,":[16],"many":[18,117,168],"other":[19],"areas.":[20],"In":[21,146],"this":[22,65,79],"paper,":[23],"we":[24,81,87],"begin":[25],"the":[26,62,106,134,137,141,154,160,173],"study":[27],"of":[28,45,48,56,64,130,136,140,144,152,162,175],"how":[29],"to":[30,89,133],"exploit":[31],"chordal":[32,70,91,108],"computational":[35,155],"algebraic":[36],"geometry---in":[37],"particular,":[38,68,147],"solving":[40],"polynomial":[41,49],"systems.":[42],"The":[43,119],"a":[46,57,83,149],"system":[47],"equations":[50],"can":[51,75,110],"be":[52,76],"described":[53],"terms":[55],"graph.":[58],"By":[59,101],"carefully":[60],"exploiting":[61],"properties":[63],"graph":[66,103,138,181],"(in":[67],"its":[69],"completions),":[71],"more":[72],"algorithms":[74,115],"developed.":[77],"To":[78],"end,":[80],"develop":[82],"new":[84],"technique,":[85],"which":[86],"refer":[88],"as":[90],"elimination,":[92],"that":[93],"relies":[94],"on":[95,127],"elimination":[96,109],"theory":[97],"Gr\u00f6bner":[99,113],"bases.":[100],"maintaining":[102],"throughout":[105],"process,":[107],"outperform":[111],"standard":[112],"bases":[114],"cases.":[118],"reason":[120],"is":[121,157],"because":[122],"all":[123],"computations":[124],"are":[125],"done":[126],"\u201csmaller\u201d":[128],"rings":[129],"size":[131],"equal":[132],"(instead":[139],"total":[142],"number":[143,161],"variables).":[145],"restricted":[150],"class":[151],"ideals,":[153],"complexity":[156],"variables.":[163],"arises":[166],"relevant":[169],"applications.":[170],"We":[171],"demonstrate":[172],"suitability":[174],"our":[176],"methods":[177],"examples":[179],"from":[180],"colorings,":[182],"cryptography,":[183],"sensor":[184],"localization,":[185],"differential":[187],"equations.":[188]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
