{"id":"https://openalex.org/W2889414864","doi":"https://doi.org/10.1145/3470858","title":"Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes","display_name":"Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes","publication_year":2021,"publication_date":"2021-09-01","ids":{"openalex":"https://openalex.org/W2889414864","doi":"https://doi.org/10.1145/3470858","mag":"2889414864"},"language":"en","primary_location":{"id":"doi:10.1145/3470858","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3470858","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/288806","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062325739","display_name":"Prasad Chaugule","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Prasad Chaugule","raw_affiliation_strings":["Indian Institute of Technology Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083072245","display_name":"Nutan Limaye","orcid":"https://orcid.org/0000-0002-0238-1674"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nutan Limaye","raw_affiliation_strings":["Indian Institute of Technology Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036369543","display_name":"Aditya Varre","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Aditya Varre","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062325739"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.4439,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64374754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"4","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983999729156494,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9983999729156494,"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":0.9977999925613403,"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":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.9015913009643555},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7044768929481506},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5775725841522217},{"id":"https://openalex.org/keywords/algebra-homomorphism","display_name":"Algebra homomorphism","score":0.5654791593551636},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.5614914298057556},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.514060378074646},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4910702705383301},{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.42005422711372375},{"id":"https://openalex.org/keywords/symmetric-polynomial","display_name":"Symmetric polynomial","score":0.4150039553642273},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40766844153404236},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.36329078674316406},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.27831539511680603},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.11558794975280762},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.11000922322273254}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.9015913009643555},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7044768929481506},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5775725841522217},{"id":"https://openalex.org/C175316100","wikidata":"https://www.wikidata.org/wiki/Q3882299","display_name":"Algebra homomorphism","level":3,"score":0.5654791593551636},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.5614914298057556},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.514060378074646},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4910702705383301},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.42005422711372375},{"id":"https://openalex.org/C52153879","wikidata":"https://www.wikidata.org/wiki/Q930499","display_name":"Symmetric polynomial","level":4,"score":0.4150039553642273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40766844153404236},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36329078674316406},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.27831539511680603},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.11558794975280762},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.11000922322273254},{"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:10.1145/3470858","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3470858","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:288806","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/288806","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://infoscience.epfl.ch/record/288806","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:288806","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/288806","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://infoscience.epfl.ch/record/288806","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1232310145","https://openalex.org/W1510132008","https://openalex.org/W1576854535","https://openalex.org/W1826226336","https://openalex.org/W1841088368","https://openalex.org/W2015676876","https://openalex.org/W2026944800","https://openalex.org/W2036265926","https://openalex.org/W2140994271","https://openalex.org/W2170831059","https://openalex.org/W2247638724","https://openalex.org/W2295066773","https://openalex.org/W2311102567","https://openalex.org/W2592308996","https://openalex.org/W2611339529"],"related_works":["https://openalex.org/W2188447730","https://openalex.org/W4299430609","https://openalex.org/W1494193561","https://openalex.org/W2255360573","https://openalex.org/W1771464740","https://openalex.org/W2268629067","https://openalex.org/W2005433590","https://openalex.org/W2006186391","https://openalex.org/W1765158965","https://openalex.org/W2889414864"],"abstract_inverted_index":{"We":[0,40],"present":[1],"polynomial":[2,17,62,77,85,122],"families":[3,18,63,78,86,123],"complete":[4,64,87],"for":[5,65,88,112],"the":[6,22,27,80,121],"well-studied":[7],"algebraic":[8,107],"complexity":[9],"classes":[10],"VF,":[11,66,89,114],"VBP,":[12,67,90,115],"VP,":[13,68,117],"and":[14,35,55,60,69,91],"VNP.":[15],"The":[16,76,84],"are":[19,93,124],"based":[20],"on":[21],"homomorphism":[23],"polynomials":[24],"studied":[25],"in":[26],"recent":[28],"works":[29],"of":[30,45,74,104],"Durand":[31],"et":[32,37],"al.":[33,38],"(2014)":[34],"Mahajan":[36],"(2018).":[39],"consider":[41],"three":[42],"different":[43],"variants":[44],"graph":[46],"homomorphisms,":[47],"namely":[48],"injective":[49,56],"homomorphisms":[50,53,58],",":[51,54,59],"directed":[52,57],"obtain":[61],"VNP":[70],"under":[71,126],"each":[72],"one":[73],"these.":[75],"have":[79],"following":[81],"properties:":[82],"\u2022":[83,119],"VP":[92],"model":[94],"independent,":[95],"i.e.,":[96],"they":[97],"do":[98],"not":[99],"use":[100],"a":[101,105],"particular":[102],"instance":[103],"formula,":[106],"branching":[108],"programs,":[109],"or":[110,116],"circuit":[111],"characterising":[113],"respectively.":[118],"All":[120],"hard":[125],"p":[127],"-projections.":[128]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}