{"id":"https://openalex.org/W2735638833","doi":"https://doi.org/10.1145/3188745.3188920","title":"Fine-grained reductions from approximate counting to decision","display_name":"Fine-grained reductions from approximate counting to decision","publication_year":2018,"publication_date":"2018-06-20","ids":{"openalex":"https://openalex.org/W2735638833","doi":"https://doi.org/10.1145/3188745.3188920","mag":"2735638833"},"language":"en","primary_location":{"id":"doi:10.1145/3188745.3188920","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3188745.3188920","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/en/publications/28b06f68-7ff6-4551-8bf5-36961bfdf00a","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Holger Dell","orcid":null},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Holger Dell","raw_affiliation_strings":["Saarland University, Germany / M2CI, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University, Germany / M2CI, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":null,"display_name":"John Lapinskas","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"John Lapinskas","raw_affiliation_strings":["University of Oxford, UK"],"affiliations":[{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":null,"apc_paid":null,"fwci":0.6412,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69636976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":null,"first_page":"281","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/simple","display_name":"Simple (philosophy)","score":0.5598999857902527},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.541100025177002},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5394999980926514},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.515500009059906},{"id":"https://openalex.org/keywords/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.4862000048160553},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.48010000586509705},{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.4049000144004822},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.39570000767707825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8057000041007996},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5598999857902527},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.541100025177002},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5394999980926514},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.515500009059906},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5105999708175659},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5069000124931335},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.4862000048160553},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3799000084400177},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28209999203681946},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.2572000026702881}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/3188745.3188920","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3188745.3188920","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/28b06f68-7ff6-4551-8bf5-36961bfdf00a","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/28b06f68-7ff6-4551-8bf5-36961bfdf00a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Dell, H & Lapinskas, J A 2021, 'Fine-grained reductions from approximate counting to decision', ACM Transactions on Computation Theory, vol. 13, no. 2, 8, pp. 1. https://doi.org/10.1145/3442352","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1707.04609","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.04609","pdf_url":"https://arxiv.org/pdf/1707.04609","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:46e63536-2f78-4aeb-bf3f-19144809e770","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:46e63536-2f78-4aeb-bf3f-19144809e770","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference item"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/391c4997-1835-43cb-8f2c-e5df9e7c7933","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/391c4997-1835-43cb-8f2c-e5df9e7c7933","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dell, H & Lapinskas, J A 2018, Fine-grained reductions from approximate counting to decision. in Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery, pp. 281-288. https://doi.org/10.1145/3188745.3188920","raw_type":"contributionToPeriodical"},{"id":"doi:10.4230/oasics.sosa.2018.6","is_oa":true,"landing_page_url":"https://doi.org/10.4230/oasics.sosa.2018.6","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire/28b06f68-7ff6-4551-8bf5-36961bfdf00a","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/28b06f68-7ff6-4551-8bf5-36961bfdf00a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Dell, H & Lapinskas, J A 2021, 'Fine-grained reductions from approximate counting to decision', ACM Transactions on Computation Theory, vol. 13, no. 2, 8, pp. 1. https://doi.org/10.1145/3442352","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1171700966","display_name":null,"funder_award_id":"NSF CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1559018562","display_name":null,"funder_award_id":"CCF-1741615","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2824819309","display_name":null,"funder_award_id":"334828","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"},{"id":"https://openalex.org/G4820067761","display_name":"CAREER: Common Links in Algorithms and Complexity","funder_award_id":"1741615","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1570607879","https://openalex.org/W1985572324","https://openalex.org/W1995725694","https://openalex.org/W2014603110","https://openalex.org/W2031683606","https://openalex.org/W2042764910","https://openalex.org/W2049136377","https://openalex.org/W2049647076","https://openalex.org/W2064790310","https://openalex.org/W2084732238","https://openalex.org/W2084803275","https://openalex.org/W2092928619","https://openalex.org/W2098207812","https://openalex.org/W2102477571","https://openalex.org/W2131798840","https://openalex.org/W2137407595","https://openalex.org/W2137874581","https://openalex.org/W2180459618","https://openalex.org/W2206830592","https://openalex.org/W2401929940","https://openalex.org/W2989661724","https://openalex.org/W4213071546"],"related_works":[],"abstract_inverted_index":{"In":[0,276],"this":[1,323],"paper,":[2],"we":[3,20,72,211,262],"introduce":[4],"a":[5,42,58,199,229,303],"general":[6,165],"framework":[7,162],"for":[8,76,151,174,189,248,259,265,273],"fine-grained":[9,84,230],"reductions":[10,75,123],"of":[11,35,45,61,78,171,201,217,305,316,322],"approximate":[12,32,233,274,299],"counting":[13],"problems":[14,82,107,173],"to":[15,30,100,143,157,167,169,235,289,298,301],"their":[16],"decision":[17],"versions.":[18],"(Thus":[19],"use":[21],"an":[22,256,270],"oracle":[23],"that":[24,116,210,247,264,281,293],"decides":[25],"whether":[26],"any":[27],"witness":[28],"exists":[29],"multiplicatively":[31],"the":[33,54,66,79,86,92,148,152,172,183,215,222,238,282,290,317],"number":[34,216],"witnesses":[36],"with":[37,220],"minimal":[38],"overhead.)":[39],"This":[40],"mirrors":[41],"foundational":[43],"result":[44,60,200,208,279],"Sipser":[46],"(STOC":[47,159],"1983)":[48],"and":[49,57,91,138,203,251],"Stockmeyer":[50],"(SICOMP":[51],"1985)":[52],"in":[53,65,83,195,307],"polynomial-time":[55],"setting,":[56],"similar":[59],"M\u00fcller":[62],"(IWPEC":[63],"2006)":[64],"FPT":[67],"setting.":[68],"Using":[69],"our":[70,122,207,278],"framework,":[71],"obtain":[73],"such":[74,146],"some":[77,249],"most":[80],"important":[81],"complexity:":[85],"Orthogonal":[87,184],"Vectors":[88,185],"problem,":[89],"3SUM,":[90],"Negative-Weight":[93,153],"Triangle":[94,154],"problem":[95,155,186],"(which":[96],"is":[97,114,120,163,244,255,269,287,295,328],"closely":[98],"related":[99],"All-Pairs":[101],"Shortest":[102],"Path).":[103],"While":[104],"all":[105,252,266],"these":[106,129],"have":[108,134],"simple":[109],"algorithms":[110,178],"over":[111,187],"which":[112,175],"it":[113],"conjectured":[115],"no":[117,296],"polynomial":[118],"improvement":[119],"possible,":[121],"would":[124],"remain":[125],"interesting":[126],"even":[127],"if":[128],"conjectures":[130],"were":[131],"proved;":[132],"they":[133],"only":[135],"polylogarithmic":[136],"overhead,":[137],"can":[139,192,212],"therefore":[140],"be":[141,193],"applied":[142],"subpolynomial":[144],"improvements":[145],"as":[147,314],"n3/exp(\u0398(\u221alogn))-time":[149],"algorithm":[150,258,272,297],"due":[156],"Williams":[158,202],"2014).":[160],"Our":[161],"also":[164,227],"enough":[166],"apply":[168],"versions":[170],"more":[176],"efficient":[177],"are":[179],"known.":[180],"For":[181],"example,":[182],"GF(m)d":[188],"constant":[190],"m":[191],"solved":[194],"time":[196,308],"n\u00b7poly(d)":[197],"by":[198],"Yu":[204],"(SODA":[205],"2014);":[206],"implies":[209,280],"approximately":[213],"count":[214],"orthogonal":[218],"pairs":[219],"essentially":[221],"same":[223],"running":[224],"time.":[225],"We":[226],"provide":[228],"reduction":[231],"from":[232],"#SAT":[234],"SAT.":[236],"Suppose":[237],"Strong":[239],"Exponential":[240,283],"Time":[241,284],"Hypothesis":[242,285],"(SETH)":[243],"false,":[245],"so":[246],"1<c<2":[250],"k":[253],"there":[254,268,294],"O(cn)-time":[257],"#k-SAT.":[260,275],"Then":[261],"prove":[263],"k,":[267],"O((c+o(1))n)-time":[271],"particular,":[277],"(ETH)":[286],"equivalent":[288],"seemingly-weaker":[291],"statement":[292],"#3-SAT":[300],"within":[302],"factor":[304],"1+\u03b5":[306],"2o(n)/\u03b52":[309],"(taking":[310],"\u03b5":[311],">":[312],"0":[313],"part":[315],"input).":[318],"A":[319],"full":[320],"version":[321],"paper":[324],"containing":[325],"detailed":[326],"proofs":[327],"available":[329],"at":[330],"https://arxiv.org/abs/1707.04609.":[331]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2017-07-21T00:00:00"}
