{"id":"https://openalex.org/W3214544158","doi":"https://doi.org/10.1145/3519935.3519967","title":"A new framework for matrix discrepancy: partial coloring bounds via mirror descent","display_name":"A new framework for matrix discrepancy: partial coloring bounds via mirror descent","publication_year":2022,"publication_date":"2022-06-09","ids":{"openalex":"https://openalex.org/W3214544158","doi":"https://doi.org/10.1145/3519935.3519967","mag":"3214544158"},"language":"en","primary_location":{"id":"doi:10.1145/3519935.3519967","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3519935.3519967","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3519935.3519967","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3519935.3519967","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044591096","display_name":"Daniel Dadush","orcid":"https://orcid.org/0000-0001-5577-5012"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Daniel Dadush","raw_affiliation_strings":["CWI, Netherlands"],"affiliations":[{"raw_affiliation_string":"CWI, Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101916384","display_name":"Haotian Jiang","orcid":"https://orcid.org/0000-0002-7501-2247"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Haotian Jiang","raw_affiliation_strings":["University of Washington, USA"],"affiliations":[{"raw_affiliation_string":"University of Washington, USA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103133077","display_name":"Victor Reis","orcid":"https://orcid.org/0009-0005-9735-989X"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Victor Reis","raw_affiliation_strings":["University of Washington, USA"],"affiliations":[{"raw_affiliation_string":"University of Washington, USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044591096"],"corresponding_institution_ids":["https://openalex.org/I1341640284"],"apc_list":null,"apc_paid":null,"fwci":2.2416,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85098039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"649","last_page":"658"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9952999949455261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7055602073669434},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7036688327789307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6400964260101318},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5938335657119751},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5628796219825745},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5072154998779297},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5009632110595703},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.4737050235271454},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.45644715428352356},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.4552915692329407},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44254475831985474},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.4277515113353729},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42206236720085144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19606313109397888},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10673624277114868},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10462775826454163},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09491345286369324}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7055602073669434},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7036688327789307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6400964260101318},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5938335657119751},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5628796219825745},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5072154998779297},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5009632110595703},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.4737050235271454},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.45644715428352356},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.4552915692329407},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44254475831985474},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.4277515113353729},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42206236720085144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19606313109397888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10673624277114868},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10462775826454163},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09491345286369324},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3519935.3519967","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3519935.3519967","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3519935.3519967","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3519935.3519967","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3519935.3519967","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3519935.3519967","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1171700966","display_name":null,"funder_award_id":"NSF CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2798763028","display_name":"CAREER: The Interplay between Combinatorial Optimization and Algorithmic Convex Geometry","funder_award_id":"1749609","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4858982592","display_name":"TRIPODS+X: RES: Collaborative Research: Scaling Up Descriptive Epidemiology and Metabolic Network Models via Faster Sampling","funder_award_id":"1839116","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5193979392","display_name":null,"funder_award_id":"DMS-1839116","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7116278599","display_name":null,"funder_award_id":"CCF-1749609","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7817736591","display_name":null,"funder_award_id":"1651861","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8186134642","display_name":"Collaborative Research: AF: Medium: Fundamental Challenges in Optimization","funder_award_id":"2105772","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":null},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3214544158.pdf","grobid_xml":"https://content.openalex.org/works/W3214544158.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W35105443","https://openalex.org/W163909615","https://openalex.org/W784580495","https://openalex.org/W1505731132","https://openalex.org/W1518600598","https://openalex.org/W1530312010","https://openalex.org/W1599814229","https://openalex.org/W1963961606","https://openalex.org/W2011095973","https://openalex.org/W2037586880","https://openalex.org/W2056625421","https://openalex.org/W2064868049","https://openalex.org/W2080024126","https://openalex.org/W2084471691","https://openalex.org/W2088402854","https://openalex.org/W2097240805","https://openalex.org/W2131680714","https://openalex.org/W2134348739","https://openalex.org/W2140322654","https://openalex.org/W2148195034","https://openalex.org/W2149178517","https://openalex.org/W2382162305","https://openalex.org/W2499349432","https://openalex.org/W2551238896","https://openalex.org/W2552451242","https://openalex.org/W2558885861","https://openalex.org/W2562861483","https://openalex.org/W2593701861","https://openalex.org/W2744926673","https://openalex.org/W2762123710","https://openalex.org/W2787248994","https://openalex.org/W2809031166","https://openalex.org/W2888614220","https://openalex.org/W2950343740","https://openalex.org/W2963794576","https://openalex.org/W2963978809","https://openalex.org/W2964162348","https://openalex.org/W3007362474","https://openalex.org/W3042180208","https://openalex.org/W3070214604","https://openalex.org/W3088300790","https://openalex.org/W3104611862","https://openalex.org/W3150597598","https://openalex.org/W3194228126","https://openalex.org/W3205665995","https://openalex.org/W4213358110","https://openalex.org/W4230471307","https://openalex.org/W4230727657","https://openalex.org/W4232804077"],"related_works":["https://openalex.org/W2486267010","https://openalex.org/W1678820847","https://openalex.org/W2559216629","https://openalex.org/W4298096494","https://openalex.org/W1553684505","https://openalex.org/W2588465033","https://openalex.org/W2037211941","https://openalex.org/W2042403445","https://openalex.org/W2725816051","https://openalex.org/W1607707911"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,8,51,76],"Matrix":[3],"Spencer":[4],"conjecture,":[5],"we":[6,93],"study":[7],"problem":[9],"of":[10,14,45,50,75,90],"finding":[11],"signed":[12],"sums":[13],"matrices":[15,32],"with":[16,72],"a":[17,40,48,83],"small":[18],"matrix":[19],"norm.":[20],"A":[21],"well-known":[22],"strategy":[23],"to":[24,29,68],"obtain":[25],"these":[26],"signs":[27],"is":[28,66],"prove,":[30],"given":[31],"A1,":[33],"\u2026,":[34],"An":[35],"\u2208":[36,55],"\u211dm":[37],"\u00d7":[38],"m,":[39],"Gaussian":[41],"measure":[42],"lower":[43],"bound":[44],"2\u2212O(n)":[46],"for":[47],"scaling":[49],"discrepancy":[52],"body":[53],"{x":[54],"\u211dn:":[56],"||":[57],"\u2211i=1n":[58],"xi":[59],"Ai||":[60],"\u2264":[61],"1}.":[62],"We":[63],"show":[64],"this":[65],"equivalent":[67],"covering":[69],"its":[70],"polar":[71],"2O(n)":[73],"translates":[74],"cube":[77],"1/n":[78],"B\u221en,":[79],"and":[80],"construct":[81],"such":[82],"cover":[84],"via":[85],"mirror":[86],"descent.":[87],"As":[88],"applications":[89],"our":[91],"framework,":[92],"show:":[94]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}