{"id":"https://openalex.org/W2014255080","doi":"https://doi.org/10.1145/1806689.1806699","title":"Subgraph sparsification and nearly optimal ultrasparsifiers","display_name":"Subgraph sparsification and nearly optimal ultrasparsifiers","publication_year":2010,"publication_date":"2010-06-05","ids":{"openalex":"https://openalex.org/W2014255080","doi":"https://doi.org/10.1145/1806689.1806699","mag":"2014255080"},"language":"en","primary_location":{"id":"doi:10.1145/1806689.1806699","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806699","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-second ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113510025","display_name":"Alexandra Kolla","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexandra Kolla","raw_affiliation_strings":["IAS, Princeton, NJ, USA","IAS, Princeton, NJ, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"IAS, Princeton, NJ, USA","institution_ids":[]},{"raw_affiliation_string":"IAS, Princeton, NJ, USA#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068045392","display_name":"Yury Makarychev","orcid":"https://orcid.org/0000-0003-3114-3947"},"institutions":[{"id":"https://openalex.org/I160992636","display_name":"Toyota Technological Institute at Chicago","ror":"https://ror.org/02sn5gb64","country_code":"US","type":"education","lineage":["https://openalex.org/I160992636"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yury Makarychev","raw_affiliation_strings":["TTI-C, Chicago, IL, USA"],"affiliations":[{"raw_affiliation_string":"TTI-C, Chicago, IL, USA","institution_ids":["https://openalex.org/I160992636"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001035442","display_name":"Amin Saberi","orcid":"https://orcid.org/0000-0002-7043-0722"},"institutions":[{"id":"https://openalex.org/I4210137306","display_name":"Stanford Medicine","ror":"https://ror.org/03mtd9a03","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210137306","https://openalex.org/I97018004"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amin Saberi","raw_affiliation_strings":["Stanford, Stanford, CA, USA","[Stanford, Stanford, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I4210137306"]},{"raw_affiliation_string":"[Stanford, Stanford, CA, USA]","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102005063","display_name":"Shang\u2010Hua Teng","orcid":"https://orcid.org/0000-0001-5011-4514"},"institutions":[{"id":"https://openalex.org/I1342924430","display_name":"LAC+USC Medical Center","ror":"https://ror.org/04xzj3x20","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1328359107","https://openalex.org/I1342924430"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shang-Hua Teng","raw_affiliation_strings":["USC, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"USC, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1342924430"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5113510025"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":4.8431,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.95138376,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"57","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9979000091552734,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9965000152587891,"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/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.6142137050628662},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6131030917167664},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5956007242202759},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5510842204093933},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4541867971420288},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4364526867866516},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4021245241165161},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3328089118003845},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19503620266914368},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.10328167676925659},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08573564887046814}],"concepts":[{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.6142137050628662},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6131030917167664},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5956007242202759},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5510842204093933},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4541867971420288},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4364526867866516},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4021245241165161},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3328089118003845},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19503620266914368},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.10328167676925659},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08573564887046814}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1806689.1806699","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806699","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-second ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.169.7498","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.169.7498","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ttic.uchicago.edu/%7Eyury/papers/subgraphsparse.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.190.3840","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.190.3840","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stanford.edu/%7Esaberi/sparsifier.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.745.4977","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.4977","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0912.1623.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308943","display_name":"Microsoft Research","ror":"https://ror.org/00d0nc645"},{"id":"https://openalex.org/F4320336061","display_name":"Research England","ror":"https://ror.org/02wxr8x18"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1916091028","https://openalex.org/W1976125024","https://openalex.org/W1978086920","https://openalex.org/W1981745143","https://openalex.org/W1981859328","https://openalex.org/W1987717935","https://openalex.org/W2037110811","https://openalex.org/W2045107949","https://openalex.org/W2051540665","https://openalex.org/W2056532343","https://openalex.org/W2090718545","https://openalex.org/W2116673134","https://openalex.org/W2125664420","https://openalex.org/W2129575457","https://openalex.org/W2149272173","https://openalex.org/W2419092805","https://openalex.org/W2798909945","https://openalex.org/W4235946010","https://openalex.org/W6677640649","https://openalex.org/W6679129889"],"related_works":["https://openalex.org/W2032950096","https://openalex.org/W1533352539","https://openalex.org/W2266948356","https://openalex.org/W2109056537","https://openalex.org/W1519201794","https://openalex.org/W1629505938","https://openalex.org/W2767824041","https://openalex.org/W1560182867","https://openalex.org/W1987322712","https://openalex.org/W2079856162"],"abstract_inverted_index":{"We":[0,56,67],"consider":[1],"a":[2,15,23,41,50,69,78,84],"variation":[3],"of":[4,17,25,54],"the":[5,18,63,89],"spectral":[6,52],"sparsification":[7],"problem":[8,61],"where":[9],"we":[10,36],"are":[11,37],"required":[12],"to":[13,39,59,87],"keep":[14],"subgraph":[16,64],"original":[19],"graph.":[20],"Formally,":[21],"given":[22],"union":[24],"two":[26],"weighted":[27,43],"graphs":[28],"G":[29,73],"and":[30,32,74,82],"W":[31,75],"an":[33],"integer":[34],"k,":[35],"asked":[38],"find":[40,88],"k-edge":[42],"graph":[44],"Wk":[45],"such":[46,76],"that":[47,77],"G+Wk":[48],"is":[49],"good":[51,79],"sparsifer":[53],"G+W.":[55],"will":[57],"refer":[58],"this":[60],"as":[62],"(spectral)":[65],"sparsification.":[66],"present":[68],"nontrivial":[70],"condition":[71],"on":[72],"sparsifier":[80],"exists":[81],"give":[83],"polynomial-time":[85],"algorithm":[86],"sparsifer.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}