{"id":"https://openalex.org/W2098983955","doi":"https://doi.org/10.1007/s00224-012-9396-1","title":"Spectral Sparsification in the Semi-streaming Setting","display_name":"Spectral Sparsification in the Semi-streaming Setting","publication_year":2012,"publication_date":"2012-04-25","ids":{"openalex":"https://openalex.org/W2098983955","doi":"https://doi.org/10.1007/s00224-012-9396-1","mag":"2098983955"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-012-9396-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-012-9396-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://hal.archives-ouvertes.fr/hal-00573647","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022068777","display_name":"Jonathan A. Kelner","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jonathan A. Kelner","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA","Department of Mathematics Massachusetts Institute of Technology, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108553303","display_name":"A. Levin","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alex Levin","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA","Department of Mathematics Massachusetts Institute of Technology, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022068777"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":5.5286,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.96299611,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"53","issue":"2","first_page":"243","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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":0.9991000294685364,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9955000281333923,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7128020524978638},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47669050097465515},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4050294756889343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3943856954574585},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32504796981811523}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7128020524978638},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47669050097465515},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4050294756889343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3943856954574585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32504796981811523}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00224-012-9396-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-012-9396-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.188.5284","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.188.5284","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mit.edu/levin/www/pdf/semistreamingspars.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.370.127","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.370.127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://drops.dagstuhl.de/opus/volltexte/2011/3033/pdf/41.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00573647v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00573647","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Leibniz International Proceedings in Informatics (LIPIcs) series","raw_type":"\\ninfo:eu-repo/semantics/conferenceObject\\n"},{"id":"pmh:oai:HAL:hal-00573647v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00573647","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.440-451","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00573647v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00573647","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Leibniz International Proceedings in Informatics (LIPIcs) series","raw_type":"\\ninfo:eu-repo/semantics/conferenceObject\\n"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1527099827","https://openalex.org/W1618148629","https://openalex.org/W1618327071","https://openalex.org/W1967134148","https://openalex.org/W1983193888","https://openalex.org/W2045107949","https://openalex.org/W2051540665","https://openalex.org/W2053171205","https://openalex.org/W2094692193","https://openalex.org/W2125664420","https://openalex.org/W2339338500","https://openalex.org/W2467457048","https://openalex.org/W4289784826"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Let":[0],"G":[1,14,25,38,61,71,152,198],"be":[2],"a":[3,16,57,95,117,122,148,160,191,237],"graph":[4,18,136,238],"with":[5,153],"n":[6],"vertices":[7],"and":[8,72,105,171,207,269],"m":[9,44],"edges.":[10,45,250],"A":[11],"sparsifier":[12,59,118,150,193,221],"of":[13,50,60,70,87,111,140,151,165,197,214,242],"is":[15,52,56,80,159,205],"sparse":[17],"on":[19],"the":[20,63,68,84,134,163,166,183,195,220,240,247,256,289,298,309],"same":[21],"vertex":[22],"set":[23],"approximating":[24],"in":[26,231,285,301,315],"some":[27],"natural":[28,206],"way.":[29],"It":[30,251],"allows":[31],"us":[32,121,128],"to":[33,125,129,219,236,246,262,274,287,296,303],"say":[34],"useful":[35,123],"things":[36],"about":[37,133],"while":[39],"considering":[40],"much":[41],"fewer":[42],"than":[43,83],"The":[46],"strongest":[47],"commonly-used":[48],"notion":[49,79],"sparsification":[51],"spectral":[53,58,149],"sparsification;":[54],"H":[55,73,224,302],"if":[62],"quadratic":[64],"forms":[65],"induced":[66],"by":[67,312],"Laplacians":[69],"approximate":[74],"one":[75,174],"another":[76],"well.":[77],"This":[78],"strictly":[81],"stronger":[82],"earlier":[85,313],"concept":[86],"combinatorial":[88],"sparsification.":[89],"In":[90,113,178],"this":[91,114,305],"paper,":[92],"we":[93,99,106,200,211,216,228,267,271,293],"consider":[94],"semi-streaming":[96],"setting,":[97],"where":[98],"have":[100,201],"only":[101,173,308],"$\\tilde{O}(n)$":[102,232],"storage":[103],"space,":[104],"thus":[107,253],"cannot":[108],"keep":[109],"all":[110,139,189],"G.":[112,177],"case,":[115],"maintaining":[116],"instead":[119],"gives":[120],"approximation":[124],"G,":[126,215],"allowing":[127],"answer":[130],"certain":[131],"questions":[132],"original":[135],"without":[137],"storing":[138],"it.":[141],"We":[142],"introduce":[143],"an":[144],"algorithm":[145,181,204],"for":[146,194],"constructing":[147],"O(nlogn/\u03f5":[154],"2)":[155],"edges":[156,213,235,284,310],"(where":[157],"\u03f5":[158],"parameter":[161],"measuring":[162],"quality":[164],"sparsifier),":[167],"taking":[168],"$\\tilde{O}(m)$":[169],"time":[170,265],"requiring":[172],"pass":[175],"over":[176],"addition,":[179],"our":[180],"has":[182],"property":[184],"that":[185,199,255,266,270],"it":[186,230],"maintains":[187],"at":[188],"times":[190],"valid":[192],"subgraph":[196],"received.":[202],"Our":[203],"conceptually":[208],"simple.":[209],"As":[210],"read":[212],"add":[217],"them":[218],"H.":[222],"Whenever":[223],"gets":[225],"too":[226],"big,":[227],"resparsify":[229],"time.":[233,318],"Adding":[234],"changes":[239],"structure":[241],"its":[243],"sparsifier\u2019s":[244],"restriction":[245],"already":[248],"existing":[249],"would":[252,259],"seem":[254],"above":[257],"procedure":[258],"cause":[260],"errors":[261],"compound":[263],"each":[264],"resparsify,":[268],"should":[272],"need":[273],"either":[275],"retain":[276],"significantly":[277],"more":[278],"information":[279,299],"or":[280],"reexamine":[281],"previously":[282],"discarded":[283],"order":[286],"construct":[288],"new":[290],"sparsifier.":[291],"However,":[292],"show":[294],"how":[295],"use":[297],"contained":[300],"perform":[304],"resparsification":[306],"using":[307],"retained":[311],"steps":[314],"nearly":[316],"linear":[317]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}