{"id":"https://openalex.org/W1761037128","doi":"https://doi.org/10.1145/1837934.1837981","title":"The DMM bound","display_name":"The DMM bound","publication_year":2010,"publication_date":"2010-07-25","ids":{"openalex":"https://openalex.org/W1761037128","doi":"https://doi.org/10.1145/1837934.1837981","mag":"1761037128"},"language":"en","primary_location":{"id":"doi:10.1145/1837934.1837981","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837981","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00393833","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087662998","display_name":"Ioannis Z. Emiris","orcid":"https://orcid.org/0000-0002-2339-5303"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Ioannis Z. Emiris","raw_affiliation_strings":["University of Athens, Athens, Greece"],"affiliations":[{"raw_affiliation_string":"University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003683965","display_name":"Bernard Mourrain","orcid":"https://orcid.org/0000-0002-8813-1368"},"institutions":[{"id":"https://openalex.org/I4210106545","display_name":"Research Centre Inria Sophia Antipolis - M\u00e9diterran\u00e9e","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106545"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bernard Mourrain","raw_affiliation_strings":["GALAAD, INRIA M\u00e9diterran\u00e9e, Sophia-Antipolis, France"],"affiliations":[{"raw_affiliation_string":"GALAAD, INRIA M\u00e9diterran\u00e9e, Sophia-Antipolis, France","institution_ids":["https://openalex.org/I4210106545","https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002548887","display_name":"Elias Tsigaridas","orcid":"https://orcid.org/0009-0003-5015-3988"},"institutions":[{"id":"https://openalex.org/I2802335433","display_name":"Aarhus University Hospital","ror":"https://ror.org/040r8fr65","country_code":"DK","type":"healthcare","lineage":["https://openalex.org/I2802335433"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Elias P. Tsigaridas","raw_affiliation_strings":["\u00c5rhus University, Denmark"],"affiliations":[{"raw_affiliation_string":"\u00c5rhus University, Denmark","institution_ids":["https://openalex.org/I2802335433"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087662998"],"corresponding_institution_ids":["https://openalex.org/I200777214"],"apc_list":null,"apc_paid":null,"fwci":4.3584,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.94156271,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"243","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980999827384949,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.716902494430542},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.632064163684845},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6277686953544617},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5950490832328796},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5750073194503784},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4910435676574707},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.47108471393585205},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.45399388670921326},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.43198055028915405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4290658235549927},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20877110958099365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.161959707736969}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.716902494430542},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.632064163684845},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6277686953544617},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5950490832328796},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5750073194503784},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4910435676574707},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.47108471393585205},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.45399388670921326},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.43198055028915405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4290658235549927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20877110958099365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.161959707736969},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1837934.1837981","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837981","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.atira.dk:publications/4623c200-e26f-11df-a891-000ea68e967b","is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/4623c200-e26f-11df-a891-000ea68e967b","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Emiris, I Z, Mourrain, B & Tsigaridas, E 2010, 'The DMM Bound : Multivariate (Aggregrate) Separation Bounds', International Symposium on Symbolic and Algebraic Computation, pp. 243-250. https://doi.org/10.1145/1837934.1837981","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:inria-00393833v4","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00393833","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, Jul 2010, Munich, Germany. pp.243-250, &#x27E8;10.1145/1837934.1837981&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00393833v4","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00393833","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, Jul 2010, Munich, Germany. pp.243-250, &#x27E8;10.1145/1837934.1837981&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8876806070","display_name":null,"funder_award_id":"PITN-GA-2008-214584","funder_id":"https://openalex.org/F4320334960","funder_display_name":"Seventh Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320334960","display_name":"Seventh Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1483218536","https://openalex.org/W1506764403","https://openalex.org/W1516027685","https://openalex.org/W1539205156","https://openalex.org/W1552350973","https://openalex.org/W1578157337","https://openalex.org/W1625225258","https://openalex.org/W1773960385","https://openalex.org/W1976392590","https://openalex.org/W1979198195","https://openalex.org/W1981287047","https://openalex.org/W2001675075","https://openalex.org/W2011693299","https://openalex.org/W2018946319","https://openalex.org/W2021573332","https://openalex.org/W2025941018","https://openalex.org/W2032951732","https://openalex.org/W2044145252","https://openalex.org/W2067705970","https://openalex.org/W2069835786","https://openalex.org/W2076593831","https://openalex.org/W2077569399","https://openalex.org/W2105458451","https://openalex.org/W2130952444","https://openalex.org/W2158622794","https://openalex.org/W2168222442","https://openalex.org/W2559475576","https://openalex.org/W2949982965","https://openalex.org/W3102149755","https://openalex.org/W4206467752"],"related_works":["https://openalex.org/W3048214159","https://openalex.org/W2132137594","https://openalex.org/W2069783012","https://openalex.org/W2085967955","https://openalex.org/W4256335355","https://openalex.org/W3098612666","https://openalex.org/W1499116563","https://openalex.org/W2138867060","https://openalex.org/W2023859141","https://openalex.org/W2182290077"],"abstract_inverted_index":{"In":[0],"this":[1,178],"paper":[2],"we":[3,180],"derive":[4],"aggregate":[5,57],"separation":[6],"bounds,":[7],"named":[8],"after":[9],"Davenport-Mahler-Mignotte":[10],"(DMM),":[11],"on":[12,20,56,131,197],"the":[13,21,32,35,38,41,86,89,94,102,105,120,132,136,146,168,175,184,198,220],"isolated":[14],"roots":[15,212],"of":[16,34,40,48,81,88,96,104,109,135,170,200,213,224],"polynomial":[17,173,215],"systems,":[18],"specifically":[19],"minimum":[22],"distance":[23],"between":[24],"any":[25],"two":[26],"such":[27],"roots.":[28],"The":[29],"bounds":[30,59,85,130,154,185],"exploit":[31,160],"structure":[33],"system":[36],"and":[37,63,91,107,141],"height":[39],"sparse":[42],"(or":[43],"toric)":[44],"resultant":[45],"by":[46,78,139],"means":[47],"mixed":[49],"volume,":[50],"as":[51,53],"well":[52],"recent":[54,128],"advances":[55],"root":[58,137],"for":[60],"univariate":[61],"polynomials,":[62,90],"are":[64,155,163],"applicable":[65],"to":[66,101,208,219],"arbitrary":[67],"positive":[68,172],"dimensional":[69],"systems.":[70],"We":[71,124],"improve":[72,182],"upon":[73,183],"Canny's":[74],"gap":[75],"theorem":[76],"[7]":[77],"a":[79,116,150,171,192,214],"factor":[80],"O(dn-1),":[82],"where":[83],"d":[84],"degree":[87],"n":[92],"is":[93,100,122,149],"number":[95,199],"variables.":[97],"One":[98],"application":[99],"bitsize":[103],"eigenvalues":[106],"eigenvectors":[108],"an":[110],"integer":[111],"matrix,":[112],"which":[113],"also":[114,125,164,181],"yields":[115],"new":[117],"proof":[118],"that":[119,202],"problem":[121],"polynomial.":[123],"compare":[126],"against":[127],"lower":[129],"absolute":[133],"value":[134,169],"coordinates":[138],"Brownawell":[140],"Yap":[142],"[5],":[143],"obtained":[144],"under":[145],"hypothesis":[147],"there":[148],"0-dimensional":[151],"projection.":[152],"Our":[153,189],"in":[156,186,206,228],"general":[157],"comparable,":[158],"but":[159],"sparseness;":[161],"they":[162],"tighter":[165],"when":[166],"bounding":[167],"over":[174],"simplex.":[176],"For":[177],"problem,":[179],"[2,":[187],"16].":[188],"analysis":[190],"provides":[191],"precise":[193],"asymptotic":[194],"upper":[195],"bound":[196,223],"steps":[201],"subdivision-based":[203],"algorithms":[204],"perform":[205],"order":[207],"isolate":[209],"all":[210],"real":[211],"system.":[216],"This":[217],"leads":[218],"first":[221],"complexity":[222],"Milne's":[225],"algorithm":[226],"[22]":[227],"2D.":[229]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2016-06-24T00:00:00"}
