{"id":"https://openalex.org/W2523573247","doi":"https://doi.org/10.17615/jgnj-9667","title":"Topics in basis reduction and integer programming","display_name":"Topics in basis reduction and integer programming","publication_year":2019,"publication_date":"2019-08-13","ids":{"openalex":"https://openalex.org/W2523573247","doi":"https://doi.org/10.17615/jgnj-9667","mag":"2523573247"},"language":"en","primary_location":{"id":"pmh:oai:cdr.lib.unc.edu:uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","is_oa":true,"landing_page_url":"https://cdr.lib.unc.edu/record/uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","pdf_url":"https://cdr.lib.unc.edu/record/uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","source":{"id":"https://openalex.org/S4306401075","display_name":"Carolina Digital Repository (University of North Carolina at Chapel Hill)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114027177","host_organization_name":"University of North Carolina at Chapel Hill","host_organization_lineage":["https://openalex.org/I114027177"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://cdr.lib.unc.edu/record/uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023962232","display_name":"Mustafa Kemal Tural","orcid":"https://orcid.org/0000-0002-7173-7646"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tural, Mustafa Kemal","raw_affiliation_strings":["University of North Carolina at Chapel Hill"],"affiliations":[{"raw_affiliation_string":"University of North Carolina at Chapel Hill","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023962232"],"corresponding_institution_ids":["https://openalex.org/I114027177"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00357899,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/T10142","display_name":"Formal Methods in Verification","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"}}],"keywords":[{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6216949820518494},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5387903451919556},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5110324621200562},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4937063157558441},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30423787236213684},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23141315579414368}],"concepts":[{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6216949820518494},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5387903451919556},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5110324621200562},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4937063157558441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30423787236213684},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23141315579414368},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:cdr.lib.unc.edu:uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","is_oa":true,"landing_page_url":"https://cdr.lib.unc.edu/record/uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","pdf_url":"https://cdr.lib.unc.edu/record/uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","source":{"id":"https://openalex.org/S4306401075","display_name":"Carolina Digital Repository (University of North Carolina at Chapel Hill)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114027177","host_organization_name":"University of North Carolina at Chapel Hill","host_organization_lineage":["https://openalex.org/I114027177"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"mag:2523573247","is_oa":false,"landing_page_url":"https://cdr.lib.unc.edu/concern/dissertations/sx61dn05s","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null},{"id":"doi:10.17615/jgnj-9667","is_oa":true,"landing_page_url":"https://doi.org/10.17615/jgnj-9667","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"thesis"}],"best_oa_location":{"id":"pmh:oai:cdr.lib.unc.edu:uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","is_oa":true,"landing_page_url":"https://cdr.lib.unc.edu/record/uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","pdf_url":"https://cdr.lib.unc.edu/record/uuid:a7413397-b1eb-4ca3-bd26-c3ffb6033668","source":{"id":"https://openalex.org/S4306401075","display_name":"Carolina Digital Repository (University of North Carolina at Chapel Hill)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114027177","host_organization_name":"University of North Carolina at Chapel Hill","host_organization_lineage":["https://openalex.org/I114027177"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2523573247.pdf","grobid_xml":"https://content.openalex.org/works/W2523573247.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W169311193","https://openalex.org/W1008178152","https://openalex.org/W1485280854","https://openalex.org/W1527013905","https://openalex.org/W1592882366","https://openalex.org/W1834548846","https://openalex.org/W1963547452","https://openalex.org/W1970290925","https://openalex.org/W1981287047","https://openalex.org/W1989510734","https://openalex.org/W2015450103","https://openalex.org/W2022398556","https://openalex.org/W2026129593","https://openalex.org/W2032980094","https://openalex.org/W2033597899","https://openalex.org/W2036265926","https://openalex.org/W2060042885","https://openalex.org/W2070268091","https://openalex.org/W2091364465","https://openalex.org/W2100440346","https://openalex.org/W2102738679","https://openalex.org/W2105277260","https://openalex.org/W2111416661","https://openalex.org/W2116916711","https://openalex.org/W2117504940","https://openalex.org/W2129740858","https://openalex.org/W2133857440","https://openalex.org/W2150780437","https://openalex.org/W2152037116","https://openalex.org/W2175796176","https://openalex.org/W2401610261","https://openalex.org/W2917703109"],"related_works":[],"abstract_inverted_index":{"A":[0],"basis":[1,7,21,49,80,122],"reduction":[2,22,50,81],"algorithm":[3,33,51],"computes":[4],"a":[5,9,165,169,179,209,323],"reduced":[6,98],"of":[8,12,68,107,141,202,257,263,300,303,313],"lattice":[10],"consisting":[11],"short":[13],"and":[14,29,42,82,104,215,254,272,315],"nearly":[15],"orthogonal":[16],"vectors.":[17],"The":[18,124,155],"best":[19],"known":[20],"method":[23,312],"is":[24,70,274,293],"due":[25],"to":[26,52,129,227,241,248,267,285],"Lenstra,":[27],"Lenstra":[28,45],"Lov\u00e1sz":[30],"(LLL):":[31],"their":[32],"has":[34],"been":[35],"extensively":[36],"used":[37,46],"in":[38,62,79,95,135,137],"cryptography,":[39],"experimental":[40],"mathematics":[41],"integer":[43,56,83,114,143,194],"programming.":[44,84],"the":[47,55,66,87,92,102,108,148,183,189,200,203,228,232,244,258,261,290,298,301,304,311,318],"LLL":[48,97],"show":[53,197],"that":[54,198,251,265],"programming":[57,115],"problem":[58,291],"can":[59],"be":[60,247,268,286],"solved":[61],"polynomial":[63],"time":[64],"when":[65,289,317],"number":[67,262],"variables":[69],"fixed.":[71],"In":[72],"this":[73],"thesis,":[74],"we":[75,146,174,235],"study":[76],"some":[77,237],"topics":[78],"We":[85,90,110,186,196,295],"make":[86,249],"following":[88],"contributions.":[89],"unify":[91],"fundamental":[93],"inequalities":[94],"an":[96],"basis,":[99],"which":[100,118],"express":[101],"shortness":[103],"near":[105],"orthogonality":[106],"basis.":[109],"analyze":[111,147,188,297],"two":[112],"recent":[113],"reformulation":[116,125,149,190],"techniques":[117,150,191],"also":[119,133,296],"rely":[120],"on":[121,151,182,192],"reduction.":[123],"methods":[126],"are":[127,132,160,206,320],"easy":[128],"describe.":[130],"They":[131],"successful":[134],"practice":[136],"solving":[138],"several":[139],"classes":[140],"hard":[142],"programs.":[144,195],"First,":[145],"bounded":[152,193],"knapsack":[153,162],"problems.":[154],"only":[156],"analyses":[157],"so":[158],"far":[159],"for":[161,252],"problems":[163,309],"with":[164],"constraint":[166,184,204],"vector":[167],"having":[168],"certain":[170],"decomposable":[171],"structure.":[172],"Here":[173],"do":[175],"not":[176],"assume":[177],"any":[178],"priori":[180],"structure":[181],"vector.":[185],"then":[187,213],"if":[199,225],"coefficients":[201,319],"matrix":[205],"drawn":[207],"from":[208,322],"sufficiently":[210],"large":[211,243,324],"interval,":[212],"branch":[214,271,314],"bound":[216,273,316],"creates":[217],"at":[218,222,275,278],"most":[219,276],"one":[220,277],"node":[221],"each":[223,279],"level":[224],"applied":[226],"reformulated":[229,259],"instances.":[230],"On":[231],"practical":[233],"side,":[234],"give":[236],"numerical":[238],"values":[239,282],"as":[240],"how":[242],"numbers":[245],"should":[246],"sure":[250],"90":[253],"99":[255],"percent":[256],"instances,":[260],"subproblems":[264],"need":[266],"enumerated":[269],"by":[270],"level.":[280],"These":[281],"turned":[283],"out":[284],"surprisingly":[287],"small":[288],"size":[292],"moderate.":[294],"solvability":[299],"``majority":[302],"low":[305],"density":[306],"subset":[307],"sum":[308],"using":[310],"chosen":[321],"interval.":[325]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}