{"id":"https://openalex.org/W2118228880","doi":"https://doi.org/10.1145/1806689.1806721","title":"Optimal homologous cycles, total unimodularity, and linear programming","display_name":"Optimal homologous cycles, total unimodularity, and linear programming","publication_year":2010,"publication_date":"2010-06-05","ids":{"openalex":"https://openalex.org/W2118228880","doi":"https://doi.org/10.1145/1806689.1806721","mag":"2118228880"},"language":"en","primary_location":{"id":"doi:10.1145/1806689.1806721","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-second ACM symposium on Theory of computing","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/A5025354167","display_name":"Tamal K. Dey","orcid":"https://orcid.org/0000-0001-5160-9738"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tamal K. Dey","raw_affiliation_strings":["The Ohio State University, Columbus, OH, USA","The Ohio State University, Columbus, OH, USA.;"],"affiliations":[{"raw_affiliation_string":"The Ohio State University, Columbus, OH, USA","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"The Ohio State University, Columbus, OH, USA.;","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016423606","display_name":"Anil N. Hirani","orcid":"https://orcid.org/0000-0003-3506-1703"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anil N. Hirani","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, Champaign, IL, USA","University of Illinois at Urbana-Champaign, Champaign, IL, USA;"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Champaign, IL, USA;","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102955818","display_name":"Bala Krishnamoorthy","orcid":"https://orcid.org/0000-0002-2727-6547"},"institutions":[{"id":"https://openalex.org/I72951846","display_name":"Washington State University","ror":"https://ror.org/05dk0ce17","country_code":"US","type":"education","lineage":["https://openalex.org/I72951846"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bala Krishnamoorthy","raw_affiliation_strings":["Washington State University, Pullman, WA, USA"],"affiliations":[{"raw_affiliation_string":"Washington State University, Pullman, WA, USA","institution_ids":["https://openalex.org/I72951846"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025354167"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":1.3381,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.81539831,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"221","last_page":"230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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/T12536","display_name":"Topological and Geometric Data Analysis","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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/unimodular-matrix","display_name":"Unimodular matrix","score":0.942922830581665},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.864020824432373},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7108079195022583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.683691143989563},{"id":"https://openalex.org/keywords/simplicial-homology","display_name":"Simplicial homology","score":0.6043724417686462},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.4576493799686432},{"id":"https://openalex.org/keywords/homologous-chromosome","display_name":"Homologous chromosome","score":0.4566383361816406},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.43890896439552307},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.4232890009880066},{"id":"https://openalex.org/keywords/simplicial-approximation-theorem","display_name":"Simplicial approximation theorem","score":0.41267022490501404},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4081726372241974},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21061977744102478},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12578335404396057},{"id":"https://openalex.org/keywords/simplicial-set","display_name":"Simplicial set","score":0.12488526105880737},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07791405916213989},{"id":"https://openalex.org/keywords/amino-acid","display_name":"Amino acid","score":0.06531459093093872},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.060184478759765625}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.942922830581665},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.864020824432373},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7108079195022583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.683691143989563},{"id":"https://openalex.org/C3469331","wikidata":"https://www.wikidata.org/wiki/Q7520902","display_name":"Simplicial homology","level":3,"score":0.6043724417686462},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.4576493799686432},{"id":"https://openalex.org/C64894306","wikidata":"https://www.wikidata.org/wiki/Q849622","display_name":"Homologous chromosome","level":3,"score":0.4566383361816406},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.43890896439552307},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.4232890009880066},{"id":"https://openalex.org/C64245159","wikidata":"https://www.wikidata.org/wiki/Q3983972","display_name":"Simplicial approximation theorem","level":5,"score":0.41267022490501404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4081726372241974},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21061977744102478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12578335404396057},{"id":"https://openalex.org/C155366967","wikidata":"https://www.wikidata.org/wiki/Q1467124","display_name":"Simplicial set","level":4,"score":0.12488526105880737},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07791405916213989},{"id":"https://openalex.org/C515207424","wikidata":"https://www.wikidata.org/wiki/Q8066","display_name":"Amino acid","level":2,"score":0.06531459093093872},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.060184478759765625},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"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/C90856448","wikidata":"https://www.wikidata.org/wiki/Q431","display_name":"Zoology","level":1,"score":0.0},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1806689.1806721","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-second ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1496383623","https://openalex.org/W1762430620","https://openalex.org/W1963547452","https://openalex.org/W1972577005","https://openalex.org/W1972872923","https://openalex.org/W1976067114","https://openalex.org/W1991566340","https://openalex.org/W2005356779","https://openalex.org/W2026605623","https://openalex.org/W2040101882","https://openalex.org/W2045867632","https://openalex.org/W2066108505","https://openalex.org/W2093766264","https://openalex.org/W2103985627","https://openalex.org/W2110221038","https://openalex.org/W2118382603","https://openalex.org/W2130458586","https://openalex.org/W2135957449","https://openalex.org/W2150154671","https://openalex.org/W2199785256","https://openalex.org/W2486762503","https://openalex.org/W3013843370","https://openalex.org/W3107709063","https://openalex.org/W4245335543","https://openalex.org/W4301808069","https://openalex.org/W6629795034","https://openalex.org/W6637924259","https://openalex.org/W6786071171","https://openalex.org/W6996888795"],"related_works":["https://openalex.org/W4288359443","https://openalex.org/W2969857904","https://openalex.org/W2943582562","https://openalex.org/W1992772797","https://openalex.org/W230527091","https://openalex.org/W2399269288","https://openalex.org/W4386942271","https://openalex.org/W4206371202","https://openalex.org/W4301866047","https://openalex.org/W4226073280"],"abstract_inverted_index":{"Given":[0],"a":[1,10,47],"simplicial":[2,49],"complex":[3,50],"with":[4,22,38],"weights":[5],"on":[6,13],"its":[7],"simplices,":[8],"and":[9,65,83],"nontrivial":[11],"cycle":[12,21],"it,":[14],"we":[15,42],"are":[16],"interested":[17],"in":[18,78],"finding":[19],"the":[20,29,34,44,57],"minimal":[23],"weight":[24],"which":[25],"is":[26,36,61,70],"homologous":[27],"to":[28],"given":[30],"one.":[31],"Assuming":[32],"that":[33],"homology":[35],"defined":[37],"integer":[39],"(Z)":[40],"coefficients,":[41],"show":[43],"following:":[45],"For":[46],"finite":[48],"K":[51,79],"of":[52,80],"dimension":[53],"greater":[54],"than":[55],"p,":[56],"boundary":[58],"matrix":[59],"[partialp+1]":[60],"totally":[62],"unimodular":[63],"if":[64,67],"only":[66],"Hp(L,":[68],"L0)":[69],"torsion-free,":[71],"for":[72],"all":[73],"pure":[74],"subcomplexes":[75],"L0,":[76],"L":[77],"dimensions":[81],"p":[82],"p+1":[84],"respectively,":[85],"where":[86],"L0":[87],"\u2282":[88],"L.":[89]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
