{"id":"https://openalex.org/W4303648898","doi":"https://doi.org/10.48550/arxiv.2210.03055","title":"Fully Lattice-Linear Algorithms","display_name":"Fully Lattice-Linear Algorithms","publication_year":2022,"publication_date":"2022-10-06","ids":{"openalex":"https://openalex.org/W4303648898","doi":"https://doi.org/10.48550/arxiv.2210.03055"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2210.03055","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2210.03055","pdf_url":"https://arxiv.org/pdf/2210.03055","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2210.03055","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046572860","display_name":"Arya Tanmay Gupta","orcid":"https://orcid.org/0000-0003-2147-8276"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gupta, Arya Tanmay","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072787717","display_name":"Sandeep S. Kulkarni","orcid":"https://orcid.org/0000-0002-7608-2116"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kulkarni, Sandeep S","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046572860"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.953000009059906,"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/T10142","display_name":"Formal Methods in Verification","score":0.953000009059906,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9380999803543091,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10661","display_name":"biodegradable polymer synthesis and properties","score":0.9175000190734863,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6359970569610596},{"id":"https://openalex.org/keywords/reciprocal-lattice","display_name":"Reciprocal lattice","score":0.5808466672897339},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5039450526237488},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.4681829512119293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4660082459449768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46376630663871765},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.4630216956138611},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4545551538467407},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.4451286196708679},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4117776155471802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35720592737197876},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12081986665725708}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6359970569610596},{"id":"https://openalex.org/C89957378","wikidata":"https://www.wikidata.org/wiki/Q164129","display_name":"Reciprocal lattice","level":3,"score":0.5808466672897339},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5039450526237488},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.4681829512119293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4660082459449768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46376630663871765},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.4630216956138611},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4545551538467407},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.4451286196708679},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4117776155471802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35720592737197876},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12081986665725708},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2210.03055","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2210.03055","pdf_url":"https://arxiv.org/pdf/2210.03055","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2210.03055","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2210.03055","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2210.03055","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2210.03055","pdf_url":"https://arxiv.org/pdf/2210.03055","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4303648898.pdf","grobid_xml":"https://content.openalex.org/works/W4303648898.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3112306103","https://openalex.org/W2949749387","https://openalex.org/W1597211008","https://openalex.org/W1819927718","https://openalex.org/W3187275826","https://openalex.org/W4390571163","https://openalex.org/W4378220036","https://openalex.org/W2071893554","https://openalex.org/W2348168089","https://openalex.org/W166611642"],"abstract_inverted_index":{"Lattice-linearity":[0],"was":[1,70],"introduced":[2],"as":[3,147,270],"a":[4,13,47,106,114,148,239,256,267],"way":[5],"to":[6,52,216,223,236],"model":[7],"problems":[8,30,63,125],"using":[9],"predicates":[10],"that":[11,32,43,151,235],"induce":[12,86],"lattice":[14,36,269],"among":[15],"the":[16,38,50,74,95,100,110,136,152,198,214,224,229,253],"global":[17,111,259],"states":[18,112,260],"(Garg,":[19],"SPAA":[20],"2020).":[21],"A":[22],"key":[23],"property":[24],"of":[25,76,94,255,258],"\\textit{the":[26],"predicate}":[27],"representing":[28],"such":[29,46],"is":[31],"it":[33],"induces":[34],"\\textit{one}":[35],"in":[37,91,194,203,228,249],"state":[39,96,139],"space.":[40],"An":[41],"algorithm":[42,199],"emerges":[44],"from":[45],"predicate":[48,107],"guarantees":[49],"execution":[51,153],"be":[53,103,245,263],"correct":[54,155],"even":[55,98,156],"if":[56,157],"nodes":[57,158,215],"execute":[58,159,217],"asynchronously.":[59,160,218],"However,":[60],"many":[61],"interesting":[62],"do":[64],"not":[65,262],"exhibit":[66],"lattice-linearity.":[67],"This":[68,116],"issue":[69],"somewhat":[71],"alleviated":[72],"with":[73],"introduction":[75],"eventually":[77],"lattice-linear":[78,124,131,165],"algorithms":[79,134,167,187,207,226],"(Gupta":[80],"and":[81,121,126,146,180,191,197],"Kulkarni,":[82],"SSS":[83],"2021).":[84],"They":[85,219],"\\textit{single}":[87],"or":[88,143],"\\textit{multiple}":[89],"lattices":[90],"\\textit{a":[92],"subset":[93],"space}":[97],"when":[99],"problem":[101],"cannot":[102],"defined":[104],"by":[105,272],"under":[108],"which":[109],"form":[113],"lattice.":[115],"paper":[117],"focuses":[118],"on":[119],"analyzing":[120],"differentiating":[122],"between":[123],"algorithms.":[127],"We":[128],"introduce":[129],"\\textit{fully":[130],"algorithms}.":[132],"These":[133,206],"partition":[135],"\\textit{entire}":[137],"reachable":[138],"space":[140],"into":[141],"\\textit{one":[142],"more":[144,240],"lattices},":[145],"result,":[149],"ensure":[150],"remains":[154],"For":[161],"demonstration,":[162],"we":[163],"present":[164,220,227],"self-stabilizing":[166],"for":[168,188,200],"minimal":[169,176],"dominating":[170],"set":[171,183],"(MDS),":[172],"graph":[173],"colouring":[174],"(GC),":[175],"vertex":[177],"cover":[178],"(MVC)":[179],"maximal":[181],"independent":[182],"(MIS)":[184],"problems.":[185],"The":[186],"MDS,":[189],"MVC":[190],"MIS":[192],"converge":[193],"$n$":[195],"moves":[196],"GC":[201],"converges":[202],"$n+2m$":[204],"moves.":[205],"preserve":[208],"this":[209,250],"time":[210],"complexity":[211],"while":[212],"allowing":[213],"an":[221],"improvement":[222],"existing":[225],"literature.":[230],"Our":[231],"work":[232],"also":[233],"demonstrates":[234],"allow":[237],"asynchrony,":[238],"relaxed":[241],"data":[242],"structure":[243],"can":[244],"allowed":[246],"(called":[247],"$\\prec$-lattice":[248],"paper,":[251],"where":[252],"meet":[254],"pair":[257],"may":[261],"defined),":[264],"rather":[265],"than":[266],"distributive":[268],"assumed":[271],"Garg.":[273]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2022-10-08T00:00:00"}