{"id":"https://openalex.org/W2030365814","doi":"https://doi.org/10.1145/1806689.1806719","title":"Detecting high log-densities","display_name":"Detecting high log-densities","publication_year":2010,"publication_date":"2010-06-05","ids":{"openalex":"https://openalex.org/W2030365814","doi":"https://doi.org/10.1145/1806689.1806719","mag":"2030365814"},"language":"en","primary_location":{"id":"doi:10.1145/1806689.1806719","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806719","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/A5014414126","display_name":"Aditya Bhaskara","orcid":"https://orcid.org/0000-0001-5505-3140"},"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":"Aditya Bhaskara","raw_affiliation_strings":["Princeton University, Princeton, NJ, USA","Princeton University , Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University , Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071016611","display_name":"Moses Charikar","orcid":"https://orcid.org/0000-0003-0807-3389"},"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":false,"raw_author_name":"Moses Charikar","raw_affiliation_strings":["Princeton University, Princeton, NJ, USA","Princeton University , Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University , Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043851880","display_name":"Eden Chlamt\u00e1\u010d","orcid":"https://orcid.org/0000-0002-0296-0107"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Eden Chlamtac","raw_affiliation_strings":["Weizmann Institute of Science, Rehovot, Israel"],"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013190102","display_name":"Uriel Feige","orcid":"https://orcid.org/0009-0006-3749-4392"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Uriel Feige","raw_affiliation_strings":["Weizmann Institute of Science, Rehovot, Israel"],"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081431077","display_name":"Aravindan Vijayaraghavan","orcid":"https://orcid.org/0000-0001-9734-3779"},"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":false,"raw_author_name":"Aravindan Vijayaraghavan","raw_affiliation_strings":["Princeton University, Princeton, NJ, USA","Princeton University , Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University , Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5014414126"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":24.6083,"has_fulltext":false,"cited_by_count":306,"citation_normalized_percentile":{"value":0.99744766,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"201","last_page":"210"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/combinatorics","display_name":"Combinatorics","score":0.7677179574966431},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6266075968742371},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.607887327671051},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5678855776786804},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5540998578071594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5431808829307556},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5425835251808167},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.5051715970039368},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.4984755516052246},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4738205671310425},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35799023509025574},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24021559953689575},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08044940233230591},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.05452537536621094}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7677179574966431},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6266075968742371},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.607887327671051},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5678855776786804},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5540998578071594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5431808829307556},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5425835251808167},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.5051715970039368},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.4984755516052246},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4738205671310425},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35799023509025574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24021559953689575},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08044940233230591},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.05452537536621094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1806689.1806719","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806719","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1571257748","https://openalex.org/W1596683029","https://openalex.org/W1972913305","https://openalex.org/W1986010539","https://openalex.org/W2010787744","https://openalex.org/W2013469283","https://openalex.org/W2034543148","https://openalex.org/W2036836182","https://openalex.org/W2068871408","https://openalex.org/W2072802070","https://openalex.org/W2088164510","https://openalex.org/W2106264302","https://openalex.org/W2108967854","https://openalex.org/W2115659887","https://openalex.org/W2150966142","https://openalex.org/W2177686805","https://openalex.org/W2977322974","https://openalex.org/W4248550452"],"related_works":["https://openalex.org/W1992104669","https://openalex.org/W1870020915","https://openalex.org/W2018076478","https://openalex.org/W1581210843","https://openalex.org/W1529390395","https://openalex.org/W1982530285","https://openalex.org/W2887154986","https://openalex.org/W2804770727","https://openalex.org/W2611723985","https://openalex.org/W1838063489"],"abstract_inverted_index":{"In":[0],"the":[1,27,38,64,67],"Densest":[2],"k-Subgraph":[3],"problem,":[4],"given":[5],"a":[6,10,17,34,55],"graph":[7],"G":[8,20],"and":[9,42,51,75],"parameter":[11],"k,":[12],"one":[13],"needs":[14],"to":[15],"find":[16],"subgraph":[18],"of":[19,30,72,81],"induced":[21],"on":[22],"k":[23],"vertices":[24],"that":[25],"contains":[26],"largest":[28],"number":[29],"edges.":[31],"There":[32],"is":[33,49],"significant":[35],"gap":[36],"between":[37],"best":[39,69],"known":[40,70],"upper":[41],"lower":[43],"bounds":[44],"for":[45,85],"this":[46],"problem.":[47],"It":[48],"NP-hard,":[50],"does":[52],"not":[53],"have":[54],"PTAS":[56],"unless":[57],"NP":[58],"has":[59],"subexponential":[60],"time":[61],"algorithms.":[62],"On":[63],"other":[65],"hand,":[66],"current":[68],"algorithm":[71],"Feige,":[73],"Kortsarz":[74],"Peleg,":[76],"gives":[77],"an":[78],"approximation":[79],"ratio":[80],"n1/3":[82],"-":[83],"c":[84],"some":[86],"fixed":[87],"c>0":[88],"(later":[89],"estimated":[90],"at":[91],"around":[92],"c=":[93],"1/90).":[94]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":40},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":28},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":26}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}