{"id":"https://openalex.org/W2019109634","doi":"https://doi.org/10.1137/050641405","title":"A Simple Gray Code to List All Minimal Signed Binary Representations","display_name":"A Simple Gray Code to List All Minimal Signed Binary Representations","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2019109634","doi":"https://doi.org/10.1137/050641405","mag":"2019109634"},"language":"en","primary_location":{"id":"doi:10.1137/050641405","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050641405","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5060694274","display_name":"Joe Sawada","orcid":"https://orcid.org/0000-0001-7364-2993"},"institutions":[{"id":"https://openalex.org/I79817857","display_name":"University of Guelph","ror":"https://ror.org/01r7awg59","country_code":"CA","type":"education","lineage":["https://openalex.org/I79817857"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"J. Sawada","raw_affiliation_strings":["Computing and Information Science, University of Guelph, Guelph N1G 2W1, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computing and Information Science, University of Guelph, Guelph N1G 2W1, ON, Canada","institution_ids":["https://openalex.org/I79817857"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060694274"],"corresponding_institution_ids":["https://openalex.org/I79817857"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.08470626,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"1","first_page":"16","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/mathematics","display_name":"Mathematics","score":0.7960261106491089},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7694612741470337},{"id":"https://openalex.org/keywords/gray-code","display_name":"Gray code","score":0.7036047577857971},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6861491203308105},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6764007806777954},{"id":"https://openalex.org/keywords/amortized-analysis","display_name":"Amortized analysis","score":0.6166337728500366},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6089568138122559},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4867265522480011},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.46804094314575195},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23786282539367676},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.214397132396698},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.1708446741104126},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09005290269851685}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7960261106491089},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7694612741470337},{"id":"https://openalex.org/C129861397","wikidata":"https://www.wikidata.org/wiki/Q332772","display_name":"Gray code","level":2,"score":0.7036047577857971},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6861491203308105},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6764007806777954},{"id":"https://openalex.org/C142417499","wikidata":"https://www.wikidata.org/wiki/Q331716","display_name":"Amortized analysis","level":3,"score":0.6166337728500366},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6089568138122559},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4867265522480011},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46804094314575195},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23786282539367676},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.214397132396698},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.1708446741104126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09005290269851685},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050641405","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050641405","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.69.713","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.713","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.uoguelph.ca/~sawada/papers/SBR_gray.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1526011068","https://openalex.org/W1768575376","https://openalex.org/W2026445983","https://openalex.org/W2070219632","https://openalex.org/W2070557670","https://openalex.org/W2083770519","https://openalex.org/W2089047336","https://openalex.org/W2093980096","https://openalex.org/W2118428193","https://openalex.org/W2121866459","https://openalex.org/W2126209209","https://openalex.org/W2169341784"],"related_works":["https://openalex.org/W2777710427","https://openalex.org/W2040262311","https://openalex.org/W2111298487","https://openalex.org/W4298824844","https://openalex.org/W3037432008","https://openalex.org/W4298113091","https://openalex.org/W2169502127","https://openalex.org/W2019109634","https://openalex.org/W3046970181","https://openalex.org/W3009592230"],"abstract_inverted_index":{"A":[0],"signed":[1],"binary":[2,93],"representation":[3,94],"(SBR)":[4],"of":[5,26,38,58,85,91,95],"an":[6,27,59],"integer":[7,28,60],"N":[8,29,79],"is":[9,30,41,64],"a":[10,48],"string":[11],"$a_b\\cdots":[12],"a_2a_1a_0$":[13],"over":[14],"the":[15,36,76,82,89,92],"alphabet":[16],"$\\{-1,0,1\\}$":[17],"such":[18],"that":[19,80],"$N":[20],"=":[21],"\\sum_{i=0}^b":[22],"a_i2^i$.":[23],"An":[24],"SBR":[25],"said":[31],"to":[32,66],"be":[33],"minimal":[34,56,86],"if":[35],"number":[37,84],"nonzero":[39],"digits":[40],"minimum.":[42],"In":[43,72],"this":[44],"paper,":[45],"we":[46,74],"describe":[47],"simple":[49],"3\u2013close":[50],"Gray":[51],"code":[52],"for":[53,78],"listing":[54],"all":[55],"SBRs":[57,87],"N.":[61,96],"The":[62],"algorithm":[63],"implemented":[65],"run":[67],"in":[68],"constant":[69],"amortized":[70],"time.":[71],"addition,":[73],"identify":[75],"values":[77],"have":[81],"maximum":[83],"given":[88],"length":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}