{"id":"https://openalex.org/W2010916800","doi":"https://doi.org/10.1137/060656048","title":"Combination Can Be Hard: Approximability of the Unique Coverage Problem","display_name":"Combination Can Be Hard: Approximability of the Unique Coverage Problem","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2010916800","doi":"https://doi.org/10.1137/060656048","mag":"2010916800"},"language":"en","primary_location":{"id":"doi:10.1137/060656048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060656048","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-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/A5083684609","display_name":"Erik D. Demaine","orcid":"https://orcid.org/0000-0003-3803-5703"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Erik D. Demaine","raw_affiliation_strings":["edemaine@mit.edu and hajiagha@mit.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"edemaine@mit.edu and hajiagha@mit.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013190102","display_name":"Uriel Feige","orcid":"https://orcid.org/0009-0006-3749-4392"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Uriel Feige","raw_affiliation_strings":["uriel.feige@weizmann.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"uriel.feige@weizmann.ac.il#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111876448","display_name":"MohammadTaghi Hajiaghayi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"MohammadTaghi Hajiaghayi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010339836","display_name":"Mohammad R. Salavatipour","orcid":"https://orcid.org/0000-0002-7650-2045"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohammad R. Salavatipour","raw_affiliation_strings":["mreza@cs.ualberta.ca#TAB#"],"affiliations":[{"raw_affiliation_string":"mreza@cs.ualberta.ca#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083684609"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.8083,"has_fulltext":false,"cited_by_count":65,"citation_normalized_percentile":{"value":0.97441084,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"38","issue":"4","first_page":"1464","last_page":"1483"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9991000294685364,"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/T10237","display_name":"Cryptography and Data Security","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.7481889724731445},{"id":"https://openalex.org/keywords/hardness-of-approximation","display_name":"Hardness of approximation","score":0.7458892464637756},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6947125792503357},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.673321545124054},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6314334273338318},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.629538893699646},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5600940585136414},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.500220775604248},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.47541576623916626},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43473827838897705},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42118096351623535},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13012945652008057},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09924989938735962}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7481889724731445},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.7458892464637756},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6947125792503357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.673321545124054},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6314334273338318},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.629538893699646},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5600940585136414},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.500220775604248},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.47541576623916626},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43473827838897705},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42118096351623535},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13012945652008057},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09924989938735962},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060656048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060656048","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.115.8256","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.8256","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ualberta.ca/~mreza/research/unique-cover.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.391.8694","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.391.8694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://erikdemaine.org/papers/UniqueCoverage_SICOMP/paper.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1479981371","https://openalex.org/W1497071043","https://openalex.org/W1515157528","https://openalex.org/W1520010392","https://openalex.org/W1565030410","https://openalex.org/W1571257748","https://openalex.org/W1595563493","https://openalex.org/W1845642169","https://openalex.org/W1966395945","https://openalex.org/W1974888782","https://openalex.org/W1975378045","https://openalex.org/W1981696935","https://openalex.org/W1985123706","https://openalex.org/W1989234747","https://openalex.org/W2003159902","https://openalex.org/W2008755444","https://openalex.org/W2038225707","https://openalex.org/W2040441164","https://openalex.org/W2047880045","https://openalex.org/W2048454711","https://openalex.org/W2048565150","https://openalex.org/W2053651631","https://openalex.org/W2059453880","https://openalex.org/W2060363698","https://openalex.org/W2062373125","https://openalex.org/W2067936666","https://openalex.org/W2069134712","https://openalex.org/W2080379754","https://openalex.org/W2086653003","https://openalex.org/W2087038607","https://openalex.org/W2087226760","https://openalex.org/W2095713941","https://openalex.org/W2099584630","https://openalex.org/W2101622070","https://openalex.org/W2102523945","https://openalex.org/W2129846535","https://openalex.org/W2137450613","https://openalex.org/W2142458954","https://openalex.org/W2143996311","https://openalex.org/W2157377553","https://openalex.org/W2158591664","https://openalex.org/W2295428206","https://openalex.org/W2325602681","https://openalex.org/W4243637616"],"related_works":["https://openalex.org/W2131810278","https://openalex.org/W2307719096","https://openalex.org/W1561811279","https://openalex.org/W2963411648","https://openalex.org/W2952838392","https://openalex.org/W2070751425","https://openalex.org/W2016001296","https://openalex.org/W2963158951","https://openalex.org/W2019123979","https://openalex.org/W3125240838"],"abstract_inverted_index":{"We":[0,44,83,110,127],"prove":[1,37,46,65],"semilogarithmic":[2],"inapproximability":[3,39,48,68,115],"for":[4,32,40,49,90],"a":[5,12,17,70,91],"maximization":[6],"problem":[7,123],"called":[8],"unique":[9,132],"coverage:":[10],"given":[11],"collection":[13],"of":[14,23,57,76],"sets,":[15],"find":[16],"subcollection":[18],"that":[19,30,53,113],"maximizes":[20],"the":[21,74,130],"number":[22],"elements":[24],"covered":[25],"exactly":[26],"once.":[27],"Specifically,":[28],"assuming":[29,52],"$\\mathrm{NP}\\not\\subseteq\\operatorname{BPTIME}(2^{n^\\varepsilon})$":[31],"an":[33,85,98,121],"arbitrary":[34],"$\\varepsilon>0$,":[35,51],"we":[36,64],"$O(1/\\log^{\\sigma}n)$":[38],"some":[41],"constant":[42],"$\\sigma=\\sigma(\\varepsilon)$.":[43],"also":[45,111],"$O(1/\\log^{1/3-\\varepsilon}n)$":[47],"any":[50],"refuting":[54],"random":[55],"instances":[56],"3SAT":[58],"is":[59],"hard":[60],"on":[61],"average;":[62],"and":[63,96,151],"$O(1/\\log":[66],"n)$":[67],"under":[69],"plausible":[71],"hypothesis":[72],"concerning":[73],"hardness":[75],"another":[77],"problem,":[78,134],"balanced":[79],"bipartite":[80],"independent":[81],"set.":[82],"establish":[84],"$\\Omega(1/\\log":[86,99],"n)$-approximation":[87],"algorithm,":[88],"even":[89],"more":[92],"general":[93],"(budgeted)":[94,131],"setting,":[95],"obtain":[97],"B)$-approximation":[100],"algorithm":[101],"when":[102],"every":[103],"set":[104],"has":[105,139],"at":[106],"most":[107],"B":[108],"elements.":[109],"show":[112],"our":[114],"results":[116],"extend":[117],"to":[118,142],"envy-free":[119],"pricing,":[120],"important":[122],"in":[124],"computational":[125],"economics.":[126],"describe":[128],"how":[129],"coverage":[133],"motivated":[135],"by":[136],"real-world":[137],"applications,":[138],"close":[140],"connections":[141],"other":[143],"theoretical":[144],"problems,":[145],"including":[146],"max":[147],"cut,":[148],"maximum":[149],"coverage,":[150],"radio":[152],"broadcasting.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}