{"id":"https://openalex.org/W2102881115","doi":"https://doi.org/10.1109/tit.1983.1056599","title":"The largest super-increasing subset of a random set","display_name":"The largest super-increasing subset of a random set","publication_year":1983,"publication_date":"1983-01-01","ids":{"openalex":"https://openalex.org/W2102881115","doi":"https://doi.org/10.1109/tit.1983.1056599","mag":"2102881115"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1983.1056599","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056599","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5077551543","display_name":"Ehud D. Karnin","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"E. Karnin","raw_affiliation_strings":["Department of Electrical Engineering, Information System Laboratory, University of Stanford, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Information System Laboratory, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016990841","display_name":"Martin E. Hellman","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Hellman","raw_affiliation_strings":["Department of Electrical Engineering, Information System Laboratory, University of Stanford, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Information System Laboratory, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077551543"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.2585771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"29","issue":"1","first_page":"146","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9977999925613403,"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/knapsack-problem","display_name":"Knapsack problem","score":0.7678573131561279},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6064602136611938},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5420433282852173},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5362768769264221},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5188230872154236},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4765249490737915},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47082191705703735},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4588748514652252},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4235050678253174},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.380226194858551},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2786824107170105},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24711576104164124},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08955618739128113}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.7678573131561279},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6064602136611938},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5420433282852173},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5362768769264221},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5188230872154236},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4765249490737915},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47082191705703735},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4588748514652252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4235050678253174},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.380226194858551},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2786824107170105},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24711576104164124},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08955618739128113},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1983.1056599","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056599","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2011039300","https://openalex.org/W2058219874","https://openalex.org/W2106287110","https://openalex.org/W2111086843","https://openalex.org/W2150276672","https://openalex.org/W2162442687"],"related_works":["https://openalex.org/W241127407","https://openalex.org/W2381035939","https://openalex.org/W2468477307","https://openalex.org/W2910645127","https://openalex.org/W162895179","https://openalex.org/W1521824362","https://openalex.org/W3177799343","https://openalex.org/W1806182398","https://openalex.org/W3093954335","https://openalex.org/W4205482204"],"abstract_inverted_index":{"It":[0],"is":[1,24],"shown":[2],"that":[3],"the":[4,41,44],"longest":[5],"super-increasing":[6],"sequence":[7],"which":[8],"can":[9],"be":[10],"constructed":[11],"from":[12],"a":[13],"set":[14],"of":[15,35,46],"<tex":[16,29],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,30],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</tex>":[18],"independent":[19],"uniformly":[20],"distributed":[21],"random":[22],"variables":[23],"almost":[25],"surely":[26],"asymptotic":[27],"to":[28],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\log_{2}n</tex>":[31],".":[32],"Some":[33],"extensions":[34],"this":[36],"result,":[37],"as":[38,40],"well":[39],"implications":[42],"for":[43],"security":[45],"knapsack-based":[47],"cryptographic":[48],"systems,":[49],"are":[50],"discussed.":[51]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
