{"id":"https://openalex.org/W1966422755","doi":"https://doi.org/10.1145/1005285.1005301","title":"Support hull","display_name":"Support hull","publication_year":2004,"publication_date":"2004-07-04","ids":{"openalex":"https://openalex.org/W1966422755","doi":"https://doi.org/10.1145/1005285.1005301","mag":"1966422755"},"language":"en","primary_location":{"id":"doi:10.1145/1005285.1005301","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005301","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 international symposium on Symbolic and algebraic computation","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/A5079970843","display_name":"Arthur D. Chtcherba","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arthur D. Chtcherba","raw_affiliation_strings":["University of Texas - Pan American, Edinburg, TX"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas - Pan American, Edinburg, TX","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003856856","display_name":"Deepak Kapur","orcid":"https://orcid.org/0000-0003-2464-2895"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deepak Kapur","raw_affiliation_strings":["University of New Mexico, Albuquerque, NM","University of New Mexico, albuquerque, NM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, NM","institution_ids":["https://openalex.org/I169521973"]},{"raw_affiliation_string":"University of New Mexico, albuquerque, NM","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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":0.09353462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"95","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9966999888420105,"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":0.9966999888420105,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.992900013923645,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9908999800682068,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.8952544331550598},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.8140949606895447},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6355242133140564},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5942311882972717},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5722358822822571},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5010287761688232},{"id":"https://openalex.org/keywords/output-sensitive-algorithm","display_name":"Output-sensitive algorithm","score":0.4750133454799652},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4575760066509247},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.45054328441619873},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3379574418067932},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.29522061347961426},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.23727792501449585},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1810455024242401},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14899572730064392},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.12409693002700806},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.083892822265625}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8952544331550598},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.8140949606895447},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6355242133140564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5942311882972717},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5722358822822571},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5010287761688232},{"id":"https://openalex.org/C39132409","wikidata":"https://www.wikidata.org/wiki/Q7112860","display_name":"Output-sensitive algorithm","level":5,"score":0.4750133454799652},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4575760066509247},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.45054328441619873},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3379574418067932},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29522061347961426},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.23727792501449585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1810455024242401},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14899572730064392},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.12409693002700806},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.083892822265625},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1005285.1005301","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005301","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W30703437","https://openalex.org/W1828839365","https://openalex.org/W1971419216","https://openalex.org/W1979057868","https://openalex.org/W2012493593","https://openalex.org/W2018699147","https://openalex.org/W2029397348","https://openalex.org/W2043606168","https://openalex.org/W2061296216","https://openalex.org/W2063700189","https://openalex.org/W2066130115","https://openalex.org/W2067754443","https://openalex.org/W2078805441","https://openalex.org/W2084988136","https://openalex.org/W2088129367","https://openalex.org/W2201727811","https://openalex.org/W2218652040","https://openalex.org/W4285719527","https://openalex.org/W4300076833","https://openalex.org/W6638597717"],"related_works":["https://openalex.org/W2360117020","https://openalex.org/W1786647412","https://openalex.org/W2741067195","https://openalex.org/W2358001426","https://openalex.org/W2439874932","https://openalex.org/W2376290243","https://openalex.org/W1572664488","https://openalex.org/W1987576325","https://openalex.org/W3034791572","https://openalex.org/W1968489927"],"abstract_inverted_index":{"A":[0,319,365],"geometric":[1],"concept":[2,184,251],"of":[3,7,10,28,69,104,125,130,141,158,171,185,203,252,291,295,351,377],"the":[4,8,17,26,29,41,45,65,74,79,83,94,102,105,116,122,131,142,153,172,175,201,204,213,217,231,237,250,285,288,292,314,342,352,374],"support":[5,9,42,55,123,154,156,161,176,232,260,278,293,298,315,343,375],"hull":[6,43,56,86,124,157,167,177,294,344,376],"a":[11,21,138,147,159,186,221,258,296,307,323,368,378],"polynomial":[12,36,100,199,238,255,273,337,379],"was":[13],"used":[14],"earlier":[15],"by":[16,82,121,152],"authors":[18],"for":[19,33,89,196,283,321,327,331,358,361,367],"developing":[20,356],"tight":[22],"upper":[23],"bound":[24],"on":[25,73,212,355,373],"size":[27,202,286],"Cayley-Dixon":[30,46,75,117,214],"resultant":[31,47,70,91,106,148,205,363,370],"matrix":[32,149,206,371],"an":[34,61,98,197,253,271],"unmixed":[35,99,198,254,272,336],"system.":[37,239],"The":[38,54,183],"relationship":[39],"between":[40],"and":[44,67,209,345],"construction":[48,66,366],"is":[49,57,135,150,162,178,190,193,225,233,299,302,311,317,339,349,381],"analyzed":[50],"in":[51,64,136,248,279,313],"this":[52],"paper.":[53],"shown":[58],"to":[59,78,164,230,236,245,264],"play":[60],"important":[62],"role":[63,80],"analysis":[68],"matrices":[71,92,107,330],"based":[72,211,372],"formulation,":[76],"similar":[77,163],"played":[81],"associated":[84],"convex":[85,166],"(Newton":[87],"polytope)":[88],"analyzing":[90],"over":[93],"toric":[95],"variety.":[96],"For":[97],"system,":[101,200],"sizes":[103],"(both":[108,207],"dialytic":[109,208],"as":[110,112,267,269,333,335],"well":[111,268,334],"nondialytic)":[113,210],"constructed":[114],"using":[115,180,341],"formulation":[118,215],"are":[119],"determined":[120,151],"its":[126,165,346],"support.":[127],"Consequently,":[128],"degree":[129],"projection":[132],"operator":[133],"(which":[134],"general,":[137],"nontrivial":[139],"multiple":[140],"resultant)":[143],"computed":[144],"from":[145,261],"such":[146],"hull.The":[155],"given":[160,297,308],"except":[168],"that":[169,195,304],"instead":[170],"Euclidean":[173],"distance,":[174],"defined":[179],"rectilinear":[181],"distance.":[182],"support-hull":[187,226],"interior":[188,227],"point":[189,310],"introduced.":[191],"It":[192,301],"proved":[194,303],"remains":[216],"same":[218],"even":[219],"if":[220],"term":[222],"whose":[223],"exponent":[224],"with":[228,257,275],"respect":[229],"generically":[234],"added":[235],"This":[240,348],"key":[241],"insight":[242],"turned":[243],"out":[244],"be":[246],"instrumental":[247],"generalizing":[249],"system":[256,274,380],"corner-cut":[259,277],"2":[262],"dimensions":[263],"arbitrary":[265,280],"dimension":[266],"identifying":[270],"almost":[276],"dimension.An":[281],"algorithm":[282],"computing":[284,322],"(and":[287],"lattice":[289,309],"points)":[290],"presented.":[300],"determining":[305],"whether":[306],"not":[312],"hull,":[316],"NP-complete.":[318],"heuristic":[320],"good":[324],"variable":[325,359],"ordering":[326],"constructing":[328,362],"Dixon":[329],"mixed":[332],"systems":[338],"proposed":[340],"projections.":[347],"one":[350],"first":[353],"results":[354],"heuristics":[357],"orderings":[360],"matrices.":[364],"Sylvester-type":[369],"also":[382],"given.":[383]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
