{"id":"https://openalex.org/W3184850399","doi":"https://doi.org/10.4230/lipics.icalp.2021.106","title":"Knapsack and Subset Sum with Small Items.","display_name":"Knapsack and Subset Sum with Small Items.","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3184850399","doi":"https://doi.org/10.4230/lipics.icalp.2021.106","mag":"3184850399"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.4230/LIPIcs.ICALP.2021.106","pdf_url":null,"source":{"id":"https://openalex.org/S4306418971","display_name":"International Colloquium on Automata, Languages and Programming","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":[],"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/A5064315511","display_name":"Adam Polak","orcid":"https://orcid.org/0000-0003-4925-774X"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Adam Polak","raw_affiliation_strings":["Jagiellonian University, Krakow, Poland"],"affiliations":[{"raw_affiliation_string":"Jagiellonian University, Krakow, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074555680","display_name":"Lars Rohwedder","orcid":"https://orcid.org/0000-0002-9434-4589"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Lars Rohwedder","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055238529","display_name":"Karol W\u0119grzycki","orcid":"https://orcid.org/0000-0001-9746-5733"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Karol Wegrzycki","raw_affiliation_strings":["Saarland University, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institution_assertions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.451,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.675037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":76,"max":79},"biblio":{"volume":null,"issue":null,"first_page":"19","last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9975,"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"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9975,"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/T12288","display_name":"Optimization and Search Problems","score":0.9901,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9773,"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/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5518495},{"id":"https://openalex.org/keywords/subset-sum-problem","display_name":"Subset sum problem","score":0.42789066},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.42471418}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.9711546},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6831772},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5518495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5516009},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5298951},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.500432},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.46180102},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4520644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44678676},{"id":"https://openalex.org/C109275537","wikidata":"https://www.wikidata.org/wiki/Q1154420","display_name":"Subset sum problem","level":3,"score":0.42789066},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.42471418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35468978},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28193104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11649299},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.100429684},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06564051},{"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.4230/LIPIcs.ICALP.2021.106","pdf_url":null,"source":{"id":"https://openalex.org/S4306418971","display_name":"International Colloquium on Automata, Languages and Programming","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3163696105","https://openalex.org/W3082181534","https://openalex.org/W3040273797","https://openalex.org/W2952071603","https://openalex.org/W2951471734","https://openalex.org/W2951418514","https://openalex.org/W2950932535","https://openalex.org/W2901276398","https://openalex.org/W2807823634","https://openalex.org/W2804453093","https://openalex.org/W2795466116","https://openalex.org/W2621978811","https://openalex.org/W2508337090","https://openalex.org/W2502264282","https://openalex.org/W2461448377","https://openalex.org/W2154014787","https://openalex.org/W2151595466","https://openalex.org/W2027739190","https://openalex.org/W1978916761","https://openalex.org/W1580817551"],"abstract_inverted_index":{"Knapsack":[0,66],"and":[1,44,60,68,128,144,153,159,166],"Subset":[2,76],"Sum":[3,77],"are":[4],"fundamental":[5],"NP-hard":[6],"problems":[7,28],"in":[8,18,55,69,108],"combinatorial":[9],"optimization.":[10],"Recently":[11],"there":[12],"has":[13],"been":[14],"a":[15,95],"growing":[16],"interest":[17],"understanding":[19],"the":[20,39,45,65,75,82,105,109,116],"best":[21],"possible":[22],"pseudopolynomial":[23],"running":[24],"times":[25,104],"for":[26,64,74,81,138],"these":[27,112],"with":[29,87,94],"respect":[30],"to":[31,142],"various":[32],"parameters.\r\nIn":[33],"this":[34],"paper":[35],"we":[36],"focus":[37],"on":[38],"maximum":[40,46],"item":[41,47,92,106],"size":[42],"s":[43],"value":[48],"v.":[49],"We":[50],"give":[51],"algorithms":[52,79],"that":[53],"run":[54],"time":[56,70],"O(n":[57,61,71],"+":[58,62,72],"s\u00b3)":[59],"v\u00b3)":[63],"problem,":[67],"s^{5/3})":[73],"problem.\r\nOur":[78],"work":[80],"more":[83],"general":[84],"problem":[85],"variants":[86,113],"multiplicities,":[88],"where":[89],"each":[90],"input":[91],"comes":[93],"(binary":[96],"encoded)":[97],"multiplicity,":[98],"which":[99],"succinctly":[100],"describes":[101],"how":[102],"many":[103],"appears":[107],"instance.":[110],"In":[111],"n":[114],"denotes":[115],"(possibly":[117],"much":[118],"smaller)":[119],"number":[120],"of":[121,133],"distinct":[122],"items.\r\nOur":[123],"results":[124],"follow":[125],"from":[126,164],"combining":[127],"optimizing":[129],"several":[130],"diverse":[131],"lines":[132],"research,":[134],"notably":[135],"proximity":[136],"arguments":[137],"integer":[139],"programming":[140],"due":[141],"Eisenbrand":[143],"Weismantel":[145],"(TALG":[146],"2019),":[147],"fast":[148],"structured":[149],"(min,+)-convolution":[150],"by":[151],"Kellerer":[152],"Pferschy":[154],"(J.":[155],"Comb.":[156],"Optim.":[157],"2004),":[158],"additive":[160],"combinatorics":[161],"methods":[162],"originating":[163],"Galil":[165],"Margalit":[167],"(SICOMP":[168],"1991).":[169]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3184850399","counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2024-12-12T09:58:15.366525","created_date":"2021-08-02"}