{"id":"https://openalex.org/W4311064408","doi":"https://doi.org/10.1007/s10878-022-00928-0","title":"Faster algorithms for k-subset sum and variations","display_name":"Faster algorithms for k-subset sum and variations","publication_year":2022,"publication_date":"2022-12-01","ids":{"openalex":"https://openalex.org/W4311064408","doi":"https://doi.org/10.1007/s10878-022-00928-0"},"language":"lv","primary_location":{"id":"doi:10.1007/s10878-022-00928-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-022-00928-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-022-00928-0.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"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":"Journal of Combinatorial Optimization","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/s10878-022-00928-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081297062","display_name":"Antonis Antonopoulos","orcid":"https://orcid.org/0000-0002-1368-6334"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Antonis Antonopoulos","raw_affiliation_strings":["School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)","institution_ids":["https://openalex.org/I174458059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091546742","display_name":"Aris Pagourtzis","orcid":"https://orcid.org/0000-0002-6220-3722"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Aris Pagourtzis","raw_affiliation_strings":["School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)","institution_ids":["https://openalex.org/I174458059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080468106","display_name":"Stavros Petsalakis","orcid":"https://orcid.org/0000-0001-7825-2839"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Stavros Petsalakis","raw_affiliation_strings":["School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)","institution_ids":["https://openalex.org/I174458059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037706878","display_name":"Manolis Vasilakis","orcid":"https://orcid.org/0000-0001-6505-2977"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Manolis Vasilakis","raw_affiliation_strings":["School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, National Technical University of Athens, 15780, Athens, Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"NTUA - National Technical University of Athens [Athens] (Patission Complex, 42, Patission str, 10682 Athens\r\nZografou Campus - 9, Iroon Polytechniou str - 15780 Zografou, Athens - Greece)","institution_ids":["https://openalex.org/I174458059"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081297062"],"corresponding_institution_ids":["https://openalex.org/I174458059"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.6903,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71631732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"45","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9993000030517578,"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":0.9991999864578247,"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":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6362500190734863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3040784001350403}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6362500190734863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3040784001350403}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10878-022-00928-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-022-00928-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-022-00928-0.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"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":"Journal of Combinatorial Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04796321v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04796321","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Combinatorial Optimization, 2022, 45 (1), pp.24. &#x27E8;10.1007/s10878-022-00928-0&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00928-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10878-022-00928-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10878-022-00928-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-022-00928-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-022-00928-0.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"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":"Journal of Combinatorial Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2356872457","display_name":null,"funder_award_id":"Basic Research Programme, PEVE 2020","funder_id":"https://openalex.org/F4320330142","funder_display_name":"National Technical University of Athens"}],"funders":[{"id":"https://openalex.org/F4320318628","display_name":"Hellenic Academic Libraries Link","ror":null},{"id":"https://openalex.org/F4320323149","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42"},{"id":"https://openalex.org/F4320330142","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4311064408.pdf","grobid_xml":"https://content.openalex.org/works/W4311064408.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W16404204","https://openalex.org/W1485173153","https://openalex.org/W1497775426","https://openalex.org/W1514421714","https://openalex.org/W1865467296","https://openalex.org/W1990489976","https://openalex.org/W2021697340","https://openalex.org/W2053876898","https://openalex.org/W2076844787","https://openalex.org/W2085888776","https://openalex.org/W2121240598","https://openalex.org/W2127492079","https://openalex.org/W2151595466","https://openalex.org/W2169359757","https://openalex.org/W2245473852","https://openalex.org/W2401610261","https://openalex.org/W2753292724","https://openalex.org/W2765923746","https://openalex.org/W2794627135","https://openalex.org/W2885641822","https://openalex.org/W2898872836","https://openalex.org/W2910073822","https://openalex.org/W2949628502","https://openalex.org/W2952672079","https://openalex.org/W2977540477","https://openalex.org/W3035306598","https://openalex.org/W3098642663","https://openalex.org/W3099511154","https://openalex.org/W4207048092","https://openalex.org/W4214930793","https://openalex.org/W4246219036","https://openalex.org/W4285259423"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Abstract":[0],"We":[1,194,223,314],"present":[2],"new,":[3],"faster":[4,215],"pseudopolynomial":[5],"time":[6,231],"algorithms":[7,216,299,319],"for":[8,106,217],"the":[9,158,161,175,311],"k":[10,27,54,218,330,340],"-":[11,219,331,341],"Subset":[12,200,220,332,336,342,347],"Sum":[13,201,221,333,337,343,348],"problem,":[14],"defined":[15],"as":[16,207,209],"follows:":[17],"given":[18,162],"a":[19,164,227,267],"set":[20],"Z":[21],"of":[22,230,270,329],"n":[23],"positive":[24],"integers":[25],"and":[26,205,266,345],"targets":[28],"$$t_1,":[29],"\\ldots":[30,110,132],",":[31,49,79,105,111,133,334,339],"t_k$$":[32],"<mml:math":[33,61,86,113,136,180,237,274],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[34,62,87,114,137,181,238,275],"<mml:mrow>":[35,63,88,90,115,138,182,239,244,248,276,281],"<mml:msub>":[36,43,64,71,92,99,143,150],"<mml:mi>t</mml:mi>":[37,44,100,139,144,151,187,259,286],"<mml:mn>1</mml:mn>":[38,66,118,145,254],"</mml:msub>":[39,46,67,74,95,102,146,153],"<mml:mo>,</mml:mo>":[40,42,68,70,119,121,147,149],"<mml:mo>\u2026</mml:mo>":[41,120,148],"<mml:mi>k</mml:mi>":[45,73,122,152,188,249,252,260,287],"</mml:mrow>":[47,77,97,103,123,155,191,256,263,264,290,291],"</mml:math>":[48,78,104,124,156,192,265,292],"determine":[50],"whether":[51],"there":[52],"exist":[53],"disjoint":[55],"subsets":[56],"$$Z_1,\\dots":[57],",Z_k":[58],"\\subseteq":[59],"Z$$":[60],"<mml:mi>Z</mml:mi>":[65,72,76,93],"<mml:mo>\u22ef</mml:mo>":[69],"<mml:mo>\u2286</mml:mo>":[75],"such":[80],"that":[81],"$$\\Sigma":[82],"(Z_i)":[83],"=":[84,108,128],"t_i$$":[85],"<mml:mi>\u03a3</mml:mi>":[89],"<mml:mo>(</mml:mo>":[91,184,245,251,282],"<mml:mi>i</mml:mi>":[94,101,116],"<mml:mo>)</mml:mo>":[96,190,255,262,289],"<mml:mo>=</mml:mo>":[98,117,140],"$$i":[107],"1,":[109],"k$$":[112],".":[125,222,349],"Assuming":[126],"$$t":[127],"\\max":[129],"\\{":[130],"t_1,":[131],"t_k":[134],"\\}$$":[135],"<mml:mo>max</mml:mo>":[141],"<mml:mo>{</mml:mo>":[142],"<mml:mo>}</mml:mo>":[154],"is":[157],"maximum":[159],"among":[160],"targets,":[163],"standard":[165],"dynamic":[166],"programming":[167],"approach":[168],"based":[169],"on":[170,199,310],"Bellman\u2019s":[171],"algorithm":[172],"can":[173,300,320],"solve":[174],"problem":[176],"in":[177,211,303,323],"$$O(n":[178],"t^k)$$":[179,236,273],"<mml:mi>O</mml:mi>":[183,241,278],"<mml:mi>n</mml:mi>":[185,247,283],"<mml:msup>":[186,246,258,285],"</mml:msup>":[189,257,261,288],"time.":[193],"build":[195],"upon":[196],"recent":[197],"advances":[198],"due":[202],"to":[203,213,305,325],"Koiliaris":[204],"Xu,":[206],"well":[208],"Bringmann,":[210],"order":[212,304,324],"provide":[214],"devise":[224],"two":[225],"algorithms:":[226],"deterministic":[228],"one":[229,269],"complexity":[232],"$${\\tilde{O}}(n^{k":[233],"/":[234],"(k+1)}":[235],"<mml:mover>":[240,277],"<mml:mo>~</mml:mo>":[242,279],"</mml:mover>":[243,280],"<mml:mo>/</mml:mo>":[250],"<mml:mo>+</mml:mo>":[253,284],"randomised":[268],"$${\\tilde{O}}(n":[271],"+":[272],"complexity.":[293],"Additionally,":[294],"we":[295],"show":[296],"how":[297,317],"these":[298,318],"be":[301,321],"modified":[302],"incorporate":[306],"cardinality":[307],"constraints":[308],"enforced":[309],"solution":[312],"subsets.":[313],"further":[315],"demonstrate":[316],"used":[322],"cope":[326],"with":[327],"variations":[328],"namely":[335],"Ratio":[338,344],"Multiple":[346]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}