{"id":"https://openalex.org/W2368326835","doi":"https://doi.org/10.1137/16m1096402","title":"The Densest $k$-Subhypergraph Problem","display_name":"The Densest $k$-Subhypergraph Problem","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2368326835","doi":"https://doi.org/10.1137/16m1096402","mag":"2368326835"},"language":"en","primary_location":{"id":"doi:10.1137/16m1096402","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1096402","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/en/publications/79f21247-98b8-4c15-bacb-a6aa9d58c098","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043851880","display_name":"Eden Chlamt\u00e1\u010d","orcid":"https://orcid.org/0000-0002-0296-0107"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eden Chlamt\u00e1\u010d","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049161363","display_name":"Michael Dinitz","orcid":"https://orcid.org/0000-0002-2632-966X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Dinitz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054336577","display_name":"Christian Konrad","orcid":"https://orcid.org/0000-0003-1802-4011"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Konrad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056370891","display_name":"Guy Kortsarz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guy Kortsarz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015459695","display_name":"George Rabanca","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"George Rabanca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3786,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.599203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"2","first_page":"1458","last_page":"1477"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","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":0.9980000257492065,"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"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.9440647959709167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7062543630599976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6495184898376465},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.573631763458252},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49354517459869385},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.420045405626297}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.9440647959709167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7062543630599976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6495184898376465},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.573631763458252},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49354517459869385},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.420045405626297}],"mesh":[],"locations_count":11,"locations":[{"id":"doi:10.1137/16m1096402","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1096402","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/79f21247-98b8-4c15-bacb-a6aa9d58c098","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/79f21247-98b8-4c15-bacb-a6aa9d58c098","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chlamt\u00e1c, E, Dinitz, M, Konrad, C, Kortsarz, G & Rabanca, G 2018, 'The Densest $k$-Subhypergraph Problem', SIAM Journal on Discrete Mathematics, vol. 32, no. 2, pp. 1458-1477. https://doi.org/10.1137/16M1096402","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1605.04284","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.04284","pdf_url":"https://arxiv.org/pdf/1605.04284","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":"","raw_type":"text"},{"id":"mag:2368326835","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1605.04284.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:drops-oai.dagstuhl.de:6629","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.6","pdf_url":null,"source":{"id":"https://openalex.org/S4306402524","display_name":"Leibniz-Zentrum f\u00fcr Informatik (Schloss Dagstuhl)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"InProceedings"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/c2a79c08-a4ac-4b3c-aafd-62b059dbcb77","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/c2a79c08-a4ac-4b3c-aafd-62b059dbcb77","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"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":"Chlamt\u00e1c, E, Dinitz, M, Konrad, C, Kortsarz, G & Rabanca, G 2016, The Densest k-Subhypergraph Problem. in K Jansen, C Mathieu, J D P Rolim & C Umans# (eds), Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques, APPROX/RANDOM 2016, September 7-9, 2016, Paris, France. Leibniz International Proceedings in Informatics (LIPIcs), vol. 60, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, pp. 6:1-6:19. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2016.6","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/c2a79c08-a4ac-4b3c-aafd-62b059dbcb77","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/c2a79c08-a4ac-4b3c-aafd-62b059dbcb77","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"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":"Chlamt\u00e1c, E, Dinitz, M, Konrad, C, Kortsarz, G & Rabanca, G 2016, The Densest k-Subhypergraph Problem. in K Jansen, C Mathieu, J D P Rolim & C Umans# (eds), Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques, APPROX/RANDOM 2016, September 7-9, 2016, Paris, France. Leibniz International Proceedings in Informatics (LIPIcs), vol. 60, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, pp. 6:1-6:19. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2016.6","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/79f21247-98b8-4c15-bacb-a6aa9d58c098","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/79f21247-98b8-4c15-bacb-a6aa9d58c098","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Chlamt\u00e1c, E, Dinitz, M, Konrad, C, Kortsarz, G & Rabanca, G 2018, 'The Densest $k$-Subhypergraph Problem', SIAM Journal on Discrete Mathematics, vol. 32, no. 2, pp. 1458-1477. https://doi.org/10.1137/16M1096402","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/c2a79c08-a4ac-4b3c-aafd-62b059dbcb77","is_oa":true,"landing_page_url":"http://hdl.handle.net/1983/c2a79c08-a4ac-4b3c-aafd-62b059dbcb77","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"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":"Chlamt\u00e1c, E, Dinitz, M, Konrad, C, Kortsarz, G & Rabanca, G 2016, The Densest k-Subhypergraph Problem. in K Jansen, C Mathieu, J D P Rolim & C Umans# (eds), Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques, APPROX/RANDOM 2016, September 7-9, 2016, Paris, France. Leibniz International Proceedings in Informatics (LIPIcs), vol. 60, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, pp. 6:1-6:19. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2016.6","raw_type":"contributionToPeriodical"},{"id":"doi:10.48550/arxiv.1605.04284","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1605.04284","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":"Preprint"},{"id":"doi:10.4230/lipics.approx-random.2016.6","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.approx-random.2016.6","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/79f21247-98b8-4c15-bacb-a6aa9d58c098","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/79f21247-98b8-4c15-bacb-a6aa9d58c098","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chlamt\u00e1c, E, Dinitz, M, Konrad, C, Kortsarz, G & Rabanca, G 2018, 'The Densest $k$-Subhypergraph Problem', SIAM Journal on Discrete Mathematics, vol. 32, no. 2, pp. 1458-1477. https://doi.org/10.1137/16M1096402","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3046054759","display_name":null,"funder_award_id":"EP/N011163/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3440488298","display_name":"AF: Small: RUI: Network design and facility location problems","funder_award_id":"1218620","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3752371004","display_name":"CRII: AF: New Approaches to Graph Spanners","funder_award_id":"1464239","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6162709055","display_name":null,"funder_award_id":"1002/14","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G6958986694","display_name":null,"funder_award_id":"EP/D063191/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7561134949","display_name":null,"funder_award_id":"W911NF-09-2-0053","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8093936802","display_name":"BSF:2014163:Approximability of network design problems","funder_award_id":"1540547","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8657054497","display_name":"Sublinear Algorithms for Big Graphs","funder_award_id":"EP/N011163/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8944461051","display_name":"AitF: EXPL: Wide-area Dissemination under Strict Timeliness, Reliability, and Cost Constraints","funder_award_id":"1535887","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1535144194","https://openalex.org/W1599622173","https://openalex.org/W1639030016","https://openalex.org/W1972913305","https://openalex.org/W2002443286","https://openalex.org/W2017280430","https://openalex.org/W2030365814","https://openalex.org/W2036836182","https://openalex.org/W2056152695","https://openalex.org/W2072802070","https://openalex.org/W2082618810","https://openalex.org/W2091602684","https://openalex.org/W2109721451","https://openalex.org/W2112006606","https://openalex.org/W2119730666","https://openalex.org/W2151679746","https://openalex.org/W2153952206","https://openalex.org/W2181409568","https://openalex.org/W2949284379","https://openalex.org/W2952587604","https://openalex.org/W2952763838","https://openalex.org/W4302769223"],"related_works":["https://openalex.org/W2798331445","https://openalex.org/W2943467511","https://openalex.org/W1595643442","https://openalex.org/W3024354928","https://openalex.org/W1550062525","https://openalex.org/W121729551","https://openalex.org/W2953047546","https://openalex.org/W1505555274","https://openalex.org/W2951369935","https://openalex.org/W2953284642","https://openalex.org/W2734404411","https://openalex.org/W3204830310","https://openalex.org/W3193060034","https://openalex.org/W2952461506","https://openalex.org/W1968496968","https://openalex.org/W2732297087","https://openalex.org/W1921482839","https://openalex.org/W2516984173","https://openalex.org/W2962706353","https://openalex.org/W2738860453"],"abstract_inverted_index":{"The":[0],"densest":[1,95],"$k$-subgraph":[2],"(D$k$S)":[3],"problem":[4,9,98,129],"and":[5,32,41,55,86,123,188,224,232],"its":[6],"corresponding":[7],"minimization":[8],"smallest":[10],"$p$-edge":[11],"subgraph":[12],"(S$p$ES)":[13],"have":[14,159],"come":[15],"to":[16,28,33,90,114,140],"play":[17],"a":[18,37,65,100,105,131,218],"central":[19],"role":[20],"in":[21,121,146,151,200],"approximation":[22,43,67],"algorithms.":[23],"This":[24],"is":[25,57,164],"due":[26],"both":[27,84,235],"their":[29,34,147],"practical":[30],"importance":[31],"usefulness":[35],"as":[36,113,139,162],"tool":[38],"for":[39,45,186,191,198],"solving":[40],"establishing":[42],"bounds":[44],"other":[46],"problems.":[47],"These":[48],"two":[49],"problems":[50,236],"are":[51,217,227],"not":[52,63,75],"well":[53],"understood,":[54],"it":[56],"widely":[58],"believed":[59],"that":[60,234],"they":[61],"do":[62,74],"admit":[64,237],"subpolynomial":[66],"ratio":[68],"(although":[69],"the":[70,94,116,125,136,142,154,165,206,215,221,225,230],"best-known":[71],"hardness":[72],"results":[73],"rule":[76],"this":[77,80,163,170],"out).":[78],"In":[79],"paper":[81],"we":[82,172,204],"generalize":[83],"D$k$S":[85],"S$p$ES":[87],"from":[88],"graphs":[89],"hypergraphs.":[91,202],"We":[92,149,193],"consider":[93],"$k$-subhypergraph":[96],"(D$k$SH)":[97],"(given":[99,130],"hypergraph":[101],"$(V,":[102],"E)$,":[103],"find":[104],"subset":[106,219],"$W\\subseteq":[107],"V$":[108],"of":[109,118,135,144,210,220,229],"$k$":[110],"vertices":[111,145,216],"so":[112,138],"maximize":[115],"number":[117,143],"hyperedges":[119,137,158,226],"contained":[120],"$W$),":[122],"define":[124],"minimum":[126],"$p$-union":[127],"(M$p$U)":[128],"hypergraph,":[132],"choose":[133],"$p$":[134],"minimize":[141],"union).":[148],"focus":[150],"particular":[152],"on":[153,242],"case":[155,171,209],"where":[156,214],"all":[157],"size":[160],"3,":[161],"simplest":[166],"nongraph":[167],"setting.":[168],"For":[169],"provide":[173],"an":[174,189,196,238],"$O(n^{4(4-\\sqrt{3})/13":[175],"+":[176],"\\epsilon})":[177],"<":[178],"O(n^{0.697831+\\epsilon})$-approximation":[179],"(for":[180],"arbitrary":[181],"constant":[182],"$\\epsilon":[183],">":[184],"0$)":[185],"D$k$SH":[187],"$\\tilde{O}(n^{2/5})$-approximation":[190],"M$p$U.":[192],"also":[194],"give":[195],"$O(\\sqrt{m})$-approximation":[197],"M$p$U":[199],"general":[201],"Finally,":[203],"examine":[205],"interesting":[207],"special":[208],"interval":[211],"hypergraphs":[212],"(instances":[213],"natural":[222],"numbers":[223],"intervals":[228],"line)":[231],"prove":[233],"exact":[239],"polynomial-time":[240],"solution":[241],"these":[243],"instances.":[244]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}