{"id":"https://openalex.org/W2765238150","doi":"https://doi.org/10.1155/2018/7982851","title":"Evidence of Exponential Speed\u2010Up in the Solution of Hard Optimization Problems","display_name":"Evidence of Exponential Speed\u2010Up in the Solution of Hard Optimization Problems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2765238150","doi":"https://doi.org/10.1155/2018/7982851","mag":"2765238150"},"language":"en","primary_location":{"id":"doi:10.1155/2018/7982851","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/7982851","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/7982851.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/complexity/2018/7982851.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034842757","display_name":"Fabio L. Traversa","orcid":"https://orcid.org/0000-0002-5878-8115"},"institutions":[{"id":"https://openalex.org/I4210133572","display_name":"Memcomputing (United States)","ror":"https://ror.org/03cfzvy87","country_code":"US","type":"company","lineage":["https://openalex.org/I4210133572"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Fabio L. Traversa","raw_affiliation_strings":["MemComputing Inc., San Diego, CA 92130, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MemComputing Inc., San Diego, CA 92130, USA","institution_ids":["https://openalex.org/I4210133572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011991728","display_name":"Pietro Cicotti","orcid":null},"institutions":[{"id":"https://openalex.org/I181653535","display_name":"San Diego Supercomputer Center","ror":"https://ror.org/04mg3nk07","country_code":"US","type":"facility","lineage":["https://openalex.org/I181653535","https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pietro Cicotti","raw_affiliation_strings":["San Diego Supercomputer Center, La Jolla, CA 92093, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"San Diego Supercomputer Center, La Jolla, CA 92093, USA","institution_ids":["https://openalex.org/I181653535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022314625","display_name":"Forrest Sheldon","orcid":"https://orcid.org/0000-0002-7321-8364"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Forrest Sheldon","raw_affiliation_strings":["Department of Physics, University of California, La Jolla, San Diego, CA 92093, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of California, La Jolla, San Diego, CA 92093, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076782439","display_name":"Massimiliano Di Ventra","orcid":"https://orcid.org/0000-0001-9416-189X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Massimiliano Di Ventra","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9416-189X","affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034842757"],"corresponding_institution_ids":["https://openalex.org/I4210133572"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.8468,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.79542535,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"2018","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/solver","display_name":"Solver","score":0.7439706325531006},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.594109058380127},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5716593861579895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5525484085083008},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5456666350364685},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.47236233949661255},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4417315721511841},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4343392252922058},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33515575528144836}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7439706325531006},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.594109058380127},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5716593861579895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5525484085083008},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5456666350364685},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.47236233949661255},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4417315721511841},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4343392252922058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33515575528144836},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1155/2018/7982851","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/7982851","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/7982851.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1710.09278","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.09278","pdf_url":"https://arxiv.org/pdf/1710.09278","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":"mag:2765238150","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.09278.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:hin:complx:7982851","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2018/7982851.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:7066cf9345f14227b6881417b4292550","is_oa":true,"landing_page_url":"https://doaj.org/article/7066cf9345f14227b6881417b4292550","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2018 (2018)","raw_type":"article"},{"id":"doi:10.48550/arxiv.1710.09278","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.09278","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2018/7982851","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/7982851","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/7982851.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320332603","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2765238150.pdf","grobid_xml":"https://content.openalex.org/works/W2765238150.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1508206977","https://openalex.org/W1549449731","https://openalex.org/W1561953468","https://openalex.org/W1968198053","https://openalex.org/W1999032440","https://openalex.org/W2020971886","https://openalex.org/W2038569833","https://openalex.org/W2041101138","https://openalex.org/W2091628233","https://openalex.org/W2131292691","https://openalex.org/W2132228337","https://openalex.org/W2143996311","https://openalex.org/W2205573708","https://openalex.org/W2519282944","https://openalex.org/W2566505556","https://openalex.org/W2604521395","https://openalex.org/W2739607635","https://openalex.org/W2762313839","https://openalex.org/W2788512397"],"related_works":["https://openalex.org/W2963627368","https://openalex.org/W2407532194","https://openalex.org/W2612488362","https://openalex.org/W2099680089","https://openalex.org/W2030586674","https://openalex.org/W3124903127","https://openalex.org/W2154256239","https://openalex.org/W2146883452","https://openalex.org/W3104221628","https://openalex.org/W2885465588","https://openalex.org/W3174817785","https://openalex.org/W2336607827","https://openalex.org/W3094331929","https://openalex.org/W2942156587","https://openalex.org/W2404656839","https://openalex.org/W2744139284","https://openalex.org/W2903344726","https://openalex.org/W2128783315","https://openalex.org/W2009260807","https://openalex.org/W2290515589"],"abstract_inverted_index":{"Optimization":[0],"problems":[1,29,111],"pervade":[2],"essentially":[3],"every":[4],"scientific":[5],"discipline":[6],"and":[7,117,230,232,258],"industry.":[8],"A":[9],"common":[10],"form":[11],"requires":[12],"identifying":[13],"a":[14,21,91,105,135,190,206],"solution":[15,79,93],"satisfying":[16],"the":[17,41,44,47,64,77,85,122,126,131,159,162,165,180,198,201,222,225,239,243,259],"maximum":[18],"number":[19],"among":[20],"set":[22],"of":[23,43,125,139,158,194,200,208,224,242,255],"many":[24,72,267],"conflicting":[25],"constraints.":[26],"Often,":[27],"these":[28],"are":[30,80],"particularly":[31],"difficult":[32],"to":[33,59,63,76,82,108,164,252],"solve,":[34],"requiring":[35],"resources":[36],"that":[37,57,112,216,234],"grow":[38],"exponentially":[39,96],"with":[40,97,149,153,197,221],"size":[42,223],"problem.":[45],"Over":[46],"past":[48],"decades,":[49],"research":[50,69],"has":[51],"focused":[52],"on":[53,205],"developing":[54],"heuristic":[55],"approaches":[56],"attempt":[58],"find":[60],"an":[61,114],"approximation":[62,163],"solution.":[65],"However,":[66],"despite":[67],"numerous":[68],"efforts,":[70],"in":[71,228,266],"cases":[73],"even":[74],"approximations":[75,120],"optimal":[78],"hard":[81,109,209],"find,":[83],"as":[84],"computational":[86],"time":[87,229],"for":[88],"further":[89],"refining":[90],"candidate":[92],"also":[94],"grows":[95],"input":[98],"size.":[99],"In":[100],"this":[101,185,235],"paper,":[102],"we":[103,129,170],"show":[104,213],"noncombinatorial":[106],"approach":[107,248],"optimization":[110,132,210,256],"achieves":[113],"exponential":[115,186],"speed-up":[116],"finds":[118],"better":[119],"than":[121],"current":[123],"state":[124],"art.":[127],"First,":[128],"map":[130],"problem":[133,166],"into":[134],"Boolean":[136],"circuit":[137,160],"made":[138],"specially":[140],"designed,":[141],"self-organizing":[142],"logic":[143],"gates,":[144],"which":[145],"can":[146,249],"be":[147,250],"built":[148],"(nonquantum)":[150],"electronic":[151],"elements":[152],"memory.":[154],"The":[155],"equilibrium":[156,181],"points":[157],"represent":[161],"at":[167],"hand.":[168],"Then,":[169],"solve":[171],"its":[172],"associated":[173],"nonlinear":[174],"ordinary":[175],"differential":[176],"equations":[177],"numerically,":[178],"towards":[179],"points.":[182],"We":[183,212],"demonstrate":[184],"gain":[187],"by":[188],"comparing":[189],"sequential":[191],"MATLAB":[192],"implementation":[193],"our":[195,217],"solver":[196,218],"winners":[199],"2016":[202],"Max\u2010SAT":[203],"competition":[204],"variety":[207],"instances.":[211],"empirical":[214],"evidence":[215],"scales":[219],"linearly":[220],"problem,":[226],"both":[227],"memory,":[231],"argue":[233],"property":[236],"derives":[237],"from":[238],"collective":[240],"behavior":[241],"simulated":[244],"physical":[245],"circuit.":[246],"Our":[247],"applied":[251],"other":[253],"types":[254],"problems,":[257],"results":[260],"presented":[261],"here":[262],"have":[263],"far\u2010reaching":[264],"consequences":[265],"fields.":[268]},"counts_by_year":[{"year":2022,"cited_by_count":18},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
