{"id":"https://openalex.org/W4229877653","doi":"https://doi.org/10.1109/glocom.2014.7417559","title":"Topological and Algebraic Properties for Classifying Unrooted Gaussian Trees under Privacy Constraints","display_name":"Topological and Algebraic Properties for Classifying Unrooted Gaussian Trees under Privacy Constraints","publication_year":2014,"publication_date":"2014-12-01","ids":{"openalex":"https://openalex.org/W4229877653","doi":"https://doi.org/10.1109/glocom.2014.7417559"},"language":"en","primary_location":{"id":"doi:10.1109/glocom.2014.7417559","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2014.7417559","pdf_url":null,"source":{"id":"https://openalex.org/S4363607712","display_name":"2015 IEEE Global Communications Conference (GLOBECOM)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE Global Communications Conference (GLOBECOM)","raw_type":"proceedings-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/A5014229678","display_name":"Ali Moharrer","orcid":null},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Moharrer","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012143414","display_name":"Shuangqing Wei","orcid":"https://orcid.org/0000-0001-5913-1441"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuangqing Wei","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018956193","display_name":"George T. Amariucai","orcid":"https://orcid.org/0000-0003-4471-6425"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]},{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George T. Amariucai","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Iowa State University, Ames, IA, USA","School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Iowa State University, Ames, IA, USA","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101871155","display_name":"Jing Deng","orcid":"https://orcid.org/0000-0001-9286-6837"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]},{"id":"https://openalex.org/I169335092","display_name":"University of North Carolina at Greensboro","ror":"https://ror.org/04fnxsj42","country_code":"US","type":"education","lineage":["https://openalex.org/I169335092"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jing Deng","raw_affiliation_strings":["Department of Computer Science, University of North Carolina at Greensboro, Greensboro, NC, USA","School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of North Carolina at Greensboro, Greensboro, NC, USA","institution_ids":["https://openalex.org/I169335092"]},{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]}]}],"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":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31641791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9980000257492065,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9980000257492065,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.991599977016449,"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/partially-ordered-set","display_name":"Partially ordered set","score":0.721393346786499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6380044221878052},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.553134024143219},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5410074591636658},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4810464680194855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4789479374885559},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.4615914821624756},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.44870463013648987},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4291480481624603},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4207574129104614},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.42072534561157227}],"concepts":[{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.721393346786499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6380044221878052},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.553134024143219},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5410074591636658},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4810464680194855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4789479374885559},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.4615914821624756},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.44870463013648987},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4291480481624603},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4207574129104614},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.42072534561157227},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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:10.1109/glocom.2014.7417559","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2014.7417559","pdf_url":null,"source":{"id":"https://openalex.org/S4363607712","display_name":"2015 IEEE Global Communications Conference (GLOBECOM)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE Global Communications Conference (GLOBECOM)","raw_type":"proceedings-article"},{"id":"pmh:oai:repository.lsu.edu:eecs_pubs-2206","is_oa":false,"landing_page_url":"https://repository.lsu.edu/eecs_pubs/1204","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1556911442","https://openalex.org/W1603384057","https://openalex.org/W1744987284","https://openalex.org/W2008303424","https://openalex.org/W2012871268","https://openalex.org/W2022417421","https://openalex.org/W2067064328","https://openalex.org/W2074666177","https://openalex.org/W2106833918","https://openalex.org/W2108777864","https://openalex.org/W2133391651","https://openalex.org/W2153396718","https://openalex.org/W2259531055","https://openalex.org/W2963082436","https://openalex.org/W3099742098","https://openalex.org/W6637897168"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W3034924094","https://openalex.org/W3094954546","https://openalex.org/W1488708774","https://openalex.org/W2981906196","https://openalex.org/W1982811510","https://openalex.org/W4390961156","https://openalex.org/W4391100477","https://openalex.org/W4327779705","https://openalex.org/W1513698804"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"our":[3,27],"objective":[4],"is":[5,24,157],"to":[6,79,115,119,136],"find":[7],"out":[8],"how":[9],"topological":[10,57,183],"and":[11,96,181],"algebraic":[12,180],"properties":[13,58,189],"of":[14,38,152,190],"unrooted":[15],"Gaussian":[16,154,169],"tree":[17,109,121],"models":[18],"determine":[19],"their":[20],"security":[21,150],"robustness,":[22],"which":[23,73,156],"measured":[25],"by":[26],"proposed":[28],"max-min":[29,62],"information":[30,163],"(MaMI)":[31],"metric.":[32],"Such":[33],"metric":[34],"quantifies":[35],"the":[36,60,88,93,97,104,149,162],"amount":[37],"common":[39],"randomness":[40],"extractable":[41],"through":[42],"public":[43],"discussion":[44],"between":[45],"two":[46],"legitimate":[47],"nodes":[48],"under":[49,72],"an":[50,179],"eavesdropper":[51],"attack.":[52],"We":[53],"show":[54],"some":[55,187],"general":[56],"that":[59],"desired":[61],"solutions":[63],"shall":[64],"satisfy.":[65],"Under":[66],"such":[67,191],"properties,":[68],"we":[69,102,126,160],"develop":[70],"conditions":[71],"comparable":[74],"trees":[75],"are":[76],"put":[77],"together":[78],"form":[80],"partially":[81],"ordered":[82],"sets":[83],"(posets).":[84],"Each":[85],"poset":[86,94,112,140],"contains":[87],"most":[89],"favorable":[90,99],"structure":[91],"as":[92],"leader,":[95],"least":[98],"structure.":[100],"Then,":[101],"compute":[103],"Tutte-like":[105],"polynomial":[106,118],"for":[107,166],"each":[108],"in":[110,113,122,172,185],"a":[111,117,123,128,182],"order":[114],"assign":[116],"any":[120],"poset.":[124],"Moreover,":[125],"propose":[127],"novel":[129],"method,":[130],"based":[131],"on":[132],"restricted":[133],"integer":[134],"partitions,":[135],"effectively":[137],"enumerate":[138],"all":[139],"leaders.":[141],"The":[142],"results":[143],"not":[144],"only":[145],"help":[146],"us":[147,177],"understand":[148],"strength":[151],"different":[153],"trees,":[155],"critical":[158],"when":[159],"evaluate":[161],"leakage":[164],"issues":[165],"various":[167],"jointly":[168],"distributed":[170],"measurements":[171],"networks,":[173],"but":[174],"also":[175],"provide":[176],"both":[178],"perspective":[184],"grasping":[186],"fundamental":[188],"models.":[192]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}