{"id":"https://openalex.org/W3099107376","doi":null,"title":"Analysis of the Karmarkar-Karp Differencing Algorithm","display_name":"Analysis of the Karmarkar-Karp Differencing Algorithm","publication_year":null,"publication_date":null,"ids":{"openalex":"https://openalex.org/W3099107376","mag":"3099107376"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.1768","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.1768","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0802.4040v1.pdf","raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"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/A5079674772","display_name":"Stefan Boettcher","orcid":"https://orcid.org/0000-0003-1273-6771","observed_orcids":["https://orcid.org/0000-0003-1273-6771"]},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stefan Boettcher","raw_affiliation_strings":["Department of Physics, Emory University, Atlanta, GA, 30322-2430, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Emory University, Atlanta, GA, 30322-2430, USA","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004847054","display_name":"Stephan Mertens","orcid":"https://orcid.org/0000-0001-9620-0995","observed_orcids":["https://orcid.org/0000-0001-9620-0995"]},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stephan Mertens","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik, Otto-von-Guericke Universit\u00e4t, PF 4120, 39016, Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik, Otto-von-Guericke Universit\u00e4t, PF 4120, 39016, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079674772"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.453900009393692,"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":0.453900009393692,"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":0.2583000063896179,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.11469999700784683,"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/number-partitioning-problem","display_name":"number partitioning problem","score":0.906000018119812},{"id":"https://openalex.org/keywords/polynomial-time-heuristic","display_name":"polynomial-time heuristic","score":0.7409999966621399},{"id":"https://openalex.org/keywords/random-instances","display_name":"random instances","score":0.6740000247955322},{"id":"https://openalex.org/keywords/nonlinear-rate-equations","display_name":"nonlinear rate equations","score":0.9430000185966492},{"id":"https://openalex.org/keywords/performance-evaluation","display_name":"performance evaluation","score":0.6010000109672546},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"combinatorial optimization","score":0.753000020980835}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.6993933916091919},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5423553586006165},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5227413773536682},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5201061964035034},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49793291091918945},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42368248105049133},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4186337888240814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41597068309783936},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35602086782455444},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20483478903770447},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.1768","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.1768","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0802.4040v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.2516","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.2516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0802.4040v2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1566860901","https://openalex.org/W1657347807","https://openalex.org/W1984384631","https://openalex.org/W1990425868","https://openalex.org/W1990990015","https://openalex.org/W2001226941","https://openalex.org/W2011039300","https://openalex.org/W2015502562","https://openalex.org/W2019073943","https://openalex.org/W2025626074","https://openalex.org/W2034990854","https://openalex.org/W2040513782","https://openalex.org/W2083715726","https://openalex.org/W2088420962","https://openalex.org/W2090865599","https://openalex.org/W2106287110","https://openalex.org/W2123710011","https://openalex.org/W2126209209","https://openalex.org/W2148751536","https://openalex.org/W2149255574","https://openalex.org/W2153638045","https://openalex.org/W2340006107","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W7100898493","https://openalex.org/W7095110290","https://openalex.org/W2016357237","https://openalex.org/W2157300811","https://openalex.org/W1517687623","https://openalex.org/W2040513782","https://openalex.org/W7096448642","https://openalex.org/W1990990015","https://openalex.org/W7097649664","https://openalex.org/W1596439539"],"abstract_inverted_index":{"The":[0],"Karmarkar-Karp":[1],"differencing":[2,31,59],"algorithm":[3,32],"is":[4,61],"the":[5,12,27,30,54,58],"best":[6],"known":[7],"polynomial":[8],"time":[9],"heuristic":[10],"for":[11],"number":[13],"partitioning":[14],"problem,":[15],"fundamental":[16],"in":[17],"both":[18],"theoretical":[19],"computer":[20],"science":[21],"and":[22],"statistical":[23],"physics.":[24],"We":[25],"analyze":[26],"performance":[28],"of":[29,57],"on":[33],"random":[34],"instances":[35],"by":[36],"mapping":[37],"it":[38],"to":[39,63],"a":[40],"nonlinear":[41],"rate":[42],"equation.":[43],"Our":[44],"analysis":[45],"reveals":[46],"strong":[47],"finite":[48],"size":[49],"effects":[50],"that":[51],"explain":[52],"why":[53],"precise":[55],"asymptotics":[56],"solution":[60],"hard":[62],"establish":[64]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2020-11-23T00:00:00"}
