{"id":"https://openalex.org/W1739960723","doi":"https://doi.org/10.1007/11785293_12","title":"Unbiased Matrix Rounding","display_name":"Unbiased Matrix Rounding","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1739960723","doi":"https://doi.org/10.1007/11785293_12","mag":"1739960723"},"language":"en","primary_location":{"id":"doi:10.1007/11785293_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11785293_12","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5040561209","display_name":"Carola Doerr","orcid":"https://orcid.org/0000-0002-4981-3227"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Benjamin Doerr","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077389210","display_name":"Tobias Friedrich","orcid":"https://orcid.org/0000-0003-0076-6308"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Friedrich","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070076122","display_name":"Christian Klein","orcid":"https://orcid.org/0000-0001-8702-2816"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Klein","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014284164","display_name":"Ralf Osbild","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ralf Osbild","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040561209"],"corresponding_institution_ids":["https://openalex.org/I4210109712"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.5678,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.91772939,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"102","last_page":"112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.992900013923645,"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/rounding","display_name":"Rounding","score":0.9857971668243408},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.7699518203735352},{"id":"https://openalex.org/keywords/randomized-rounding","display_name":"Randomized rounding","score":0.7616435885429382},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.6681396961212158},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6594572067260742},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5442845821380615},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5350768566131592},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.5222431421279907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4443114101886749},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4196382164955139},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41278696060180664},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3832593858242035},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.16786855459213257}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.9857971668243408},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.7699518203735352},{"id":"https://openalex.org/C32029473","wikidata":"https://www.wikidata.org/wiki/Q7292010","display_name":"Randomized rounding","level":3,"score":0.7616435885429382},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.6681396961212158},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6594572067260742},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5442845821380615},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5350768566131592},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.5222431421279907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4443114101886749},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4196382164955139},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41278696060180664},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3832593858242035},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.16786855459213257},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11785293_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11785293_12","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1488521304","https://openalex.org/W1503520352","https://openalex.org/W1519375772","https://openalex.org/W1534389500","https://openalex.org/W1541025644","https://openalex.org/W1578810938","https://openalex.org/W1964119857","https://openalex.org/W1981393561","https://openalex.org/W1983621406","https://openalex.org/W1992264107","https://openalex.org/W2036194085","https://openalex.org/W2056444916","https://openalex.org/W2060164640","https://openalex.org/W2063856722","https://openalex.org/W2072123478","https://openalex.org/W2086314067","https://openalex.org/W2092554333","https://openalex.org/W2095773079","https://openalex.org/W2140414639","https://openalex.org/W2151247451","https://openalex.org/W2332944649","https://openalex.org/W2462986379","https://openalex.org/W2493844837","https://openalex.org/W2502292953","https://openalex.org/W2798301035","https://openalex.org/W3011766368","https://openalex.org/W4249495072","https://openalex.org/W4250842543","https://openalex.org/W4256664002","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2029148441","https://openalex.org/W1739960723","https://openalex.org/W2524114361","https://openalex.org/W2950115522","https://openalex.org/W2390790427","https://openalex.org/W1530375092","https://openalex.org/W2599301820","https://openalex.org/W2791474142","https://openalex.org/W2107585066","https://openalex.org/W1534389500"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}