{"id":"https://openalex.org/W4388178321","doi":"https://doi.org/10.1007/s10107-023-02026-3","title":"The limits of local search for weighted k-set packing","display_name":"The limits of local search for weighted k-set packing","publication_year":2023,"publication_date":"2023-10-28","ids":{"openalex":"https://openalex.org/W4388178321","doi":"https://doi.org/10.1007/s10107-023-02026-3"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-023-02026-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-023-02026-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-02026-3.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-02026-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060646500","display_name":"Meike Neuwohner","orcid":"https://orcid.org/0000-0002-3664-3687"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Meike Neuwohner","raw_affiliation_strings":["Research Institute for Discrete Mathematics, University of Bonn, Lenn\u00e9stra\u00dfe 2, 53113, Bonn, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3664-3687","affiliations":[{"raw_affiliation_string":"Research Institute for Discrete Mathematics, University of Bonn, Lenn\u00e9stra\u00dfe 2, 53113, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060646500"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":0.7759,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76576606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"206","issue":"1-2","first_page":"389","last_page":"427"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987999796867371,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9987999796867371,"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/T12176","display_name":"Optimization and Packing Problems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9947999715805054,"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/algorithm","display_name":"Algorithm","score":0.580802321434021},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28735870122909546}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.580802321434021},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28735870122909546}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-023-02026-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-023-02026-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-02026-3.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10107-023-02026-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-023-02026-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-02026-3.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324900","display_name":"Rheinische Friedrich-Wilhelms-Universit\u00e4t Bonn","ror":"https://ror.org/041nas322"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4388178321.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1482106463","https://openalex.org/W1582786162","https://openalex.org/W1676390513","https://openalex.org/W1923860197","https://openalex.org/W1963707128","https://openalex.org/W1966923282","https://openalex.org/W2001258629","https://openalex.org/W2030562672","https://openalex.org/W2043260929","https://openalex.org/W2079301493","https://openalex.org/W2089117840","https://openalex.org/W2140118062","https://openalex.org/W2296148711","https://openalex.org/W2327315803","https://openalex.org/W2401610261","https://openalex.org/W3138153684","https://openalex.org/W4232911618","https://openalex.org/W4285281596","https://openalex.org/W6629409943"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"consider":[2],"the":[3,54,250,267,271,334,338,396],"weighted":[4,339],"k":[5,26],"-set":[6],"packing":[7],"problem,":[8],"where,":[9],"given":[10],"a":[11,29,59,83,150,262,311,316],"collection":[12],"$${\\mathcal":[13,62],"{S}}$$":[14,63],"<mml:math":[15,37,64,87,105,154,175,195,279,351,375,422],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[16,38,65,88,106,155,176,196,280,352,376,423],"<mml:mi>S</mml:mi>":[17,42,66],"</mml:math>":[18,52,67,101,113,168,182,218,293,364,393,428],"of":[19,22,61,69,73,227,252,320,323,348,411],"sets,":[20],"each":[21],"cardinality":[23],"at":[24],"most":[25,124],",":[27,53,183,365],"and":[28,295],"positive":[30],"weight":[31,269],"function":[32],"$$w:{\\mathcal":[33],"{S}}\\rightarrow":[34],"{\\mathbb":[35],"{Q}}_{&gt;0}$$":[36],"<mml:mrow>":[39,46,89,94,107,156,158,177,197,199,209,281,283,354,377,380],"<mml:mi>w</mml:mi>":[40],"<mml:mo>:</mml:mo>":[41],"<mml:mo>\u2192</mml:mo>":[43,382],"<mml:msub>":[44,357,378,386],"<mml:mi>Q</mml:mi>":[45],"<mml:mo>&gt;</mml:mo>":[47,179],"<mml:mn>0</mml:mn>":[48,180,391],"</mml:mrow>":[49,51,97,100,112,162,167,181,203,215,217,287,292,361,384,392],"</mml:msub>":[50,360,385,389],"task":[55],"is":[56,254,276,403],"to":[57,193,259,329,337],"find":[58],"sub-collection":[60],"consisting":[68],"pairwise":[70],"disjoint":[71],"sets":[72],"maximum":[74],"total":[75],"weight.":[76],"As":[77],"this":[78,308,402],"problem":[79],"does":[80],"not":[81],"permit":[82],"polynomial-time":[84,151],"$$o(\\frac{k}{\\log":[85],"k})$$":[86],"<mml:mi>o</mml:mi>":[90],"<mml:mo>(</mml:mo>":[91],"<mml:mfrac>":[92,157,198,207,282,353,424],"<mml:mi>k</mml:mi>":[93,96,159,200,284,355,359,381,388,425],"<mml:mo>log</mml:mo>":[95],"</mml:mfrac>":[98,164,205,216,289,363,427],"<mml:mo>)</mml:mo>":[99],"-approximation":[102,169],"unless":[103],"$$P=NP$$":[104],"<mml:mi>P</mml:mi>":[108,111],"<mml:mo>=</mml:mo>":[109,390],"<mml:mi>N</mml:mi>":[110],"(Hazan":[114],"et":[115],"al.":[116],"in":[117,235,261,297,333,407],"Comput":[118],"Complex":[119],"15:20\u201339,":[120],"2006.":[121],"https://doi.org/10.1007/s00037-006-0205-6":[122],"),":[123,147],"previous":[125],"approaches":[126],"rely":[127],"on":[128,141,224,300],"local":[129,409],"search.":[130],"For":[131],"twenty":[132],"years,":[133],"Berman\u2019s":[134],"algorithm":[135,142],"SquareImp":[136,253],"(Berman,":[137],"in:":[138],"Scandinavian":[139],"workshop":[140],"theory,":[143],"Springer,":[144,303],"2000.":[145],"https://doi.org/10.1007/3-540-44985-X_19":[146],"which":[148,249],"yields":[149],"$$\\frac{k+1}{2}+\\epsilon":[152],"$$":[153,278],"<mml:mo>+</mml:mo>":[160,165,201,285,290,356],"<mml:mn>1</mml:mn>":[161,202,208,286],"<mml:mn>2</mml:mn>":[163,204,362,426],"<mml:mi>\u03f5</mml:mi>":[166,178,291,358,387],"for":[170,248,266],"any":[171],"fixed":[172],"$$\\epsilon":[173],"&gt;0$$":[174],"has":[184],"remained":[185],"unchallenged.":[186],"Only":[187],"recently,":[188],"it":[189],"could":[190],"be":[191],"improved":[192],"$$\\frac{k+1}{2}-\\frac{1}{63,700,993}$$":[194],"<mml:mo>-</mml:mo>":[206],"<mml:mn>63</mml:mn>":[210],"<mml:mo>,</mml:mo>":[211,213],"<mml:mn>700</mml:mn>":[212],"<mml:mn>993</mml:mn>":[214],"by":[219],"Neuwohner":[220],"(38th":[221],"International":[222,298],"symposium":[223,299],"theoretical":[225],"aspects":[226],"computer":[228],"science":[229],"(STACS":[230],"2021),":[231],"Leibniz":[232],"international":[233],"proceedings":[234],"informatics":[236],"(LIPIcs),":[237],"2021.":[238],"https://doi.org/10.4230/LIPIcs.STACS.2021.53":[239],").":[240,306],"In":[241,341],"her":[242],"paper,":[243],"she":[244],"showed":[245],"that":[246,401,408],"instances":[247,322],"analysis":[251,319],"almost":[255],"tight":[256],"are":[257],"\u201cclose":[258],"unweighted\u201d":[260],"certain":[263],"sense.":[264],"But":[265],"unit":[268],"variant,":[270],"best":[272,405],"known":[273],"approximation":[274,346,418],"guarantee":[275],"$$\\frac{k+1}{3}+\\epsilon":[277],"<mml:mn>3</mml:mn>":[288],"(F\u00fcrer":[294],"Yu":[296],"combinatorial":[301],"optimization,":[302],"2014.":[304],"https://doi.org/10.1007/978-3-319-09174-7_35":[305],"Using":[307],"observation":[309],"as":[310],"starting":[312],"point,":[313],"we":[314,344,399],"conduct":[315],"more":[317],"in-depth":[318],"close-to-tight":[321],"SquareImp.":[324],"This":[325],"finally":[326],"allows":[327],"us":[328],"generalize":[330],"techniques":[331],"used":[332],"unweighted":[335],"case":[336],"setting.":[340],"doing":[342],"so,":[343],"obtain":[345],"guarantees":[347],"$$\\frac{k+\\epsilon":[349],"_k}{2}$$":[350],"where":[366],"$$\\lim":[367],"_{k\\rightarrow":[368],"\\infty":[369],"}":[370],"\\epsilon":[371],"_k":[372],"=":[373],"0$$":[374],"<mml:mo>lim</mml:mo>":[379],"<mml:mi>\u221e</mml:mi>":[383],".":[394,429],"On":[395],"other":[397],"hand,":[398],"prove":[400],"asymptotically":[404],"possible":[406],"improvements":[410],"logarithmically":[412],"bounded":[413],"size":[414],"cannot":[415],"produce":[416],"an":[417],"ratio":[419],"below":[420],"$$\\frac{k}{2}$$":[421]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-02-03T23:48:18.283914","created_date":"2025-10-10T00:00:00"}