{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:28:23Z","timestamp":1768343303742,"version":"3.49.0"},"reference-count":22,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T00:00:00Z","timestamp":1684281600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Key Program of the Natural Science Foundation of the Educational Commission of Anhui Province of China","award":["2022AH050319"],"award-info":[{"award-number":["2022AH050319"]}]},{"name":"the Key Program of the Natural Science Foundation of the Educational Commission of Anhui Province of China","award":["2022AH052740"],"award-info":[{"award-number":["2022AH052740"]}]},{"name":"the Key Program of the Natural Science Foundation of the Educational Commission of Anhui Province of China","award":["2008085QF305"],"award-info":[{"award-number":["2008085QF305"]}]},{"name":"the Key Program of the Natural Science Foundation of the Educational Commission of Anhui Province of China","award":["1908085MF212"],"award-info":[{"award-number":["1908085MF212"]}]},{"name":"the Natural Science Foundation Project of Anhui Province of China","award":["2022AH050319"],"award-info":[{"award-number":["2022AH050319"]}]},{"name":"the Natural Science Foundation Project of Anhui Province of China","award":["2022AH052740"],"award-info":[{"award-number":["2022AH052740"]}]},{"name":"the Natural Science Foundation Project of Anhui Province of China","award":["2008085QF305"],"award-info":[{"award-number":["2008085QF305"]}]},{"name":"the Natural Science Foundation Project of Anhui Province of China","award":["1908085MF212"],"award-info":[{"award-number":["1908085MF212"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The differential privacy histogram publishing method based on grouping cannot balance the grouping reconstruction error and Laplace noise error, resulting in insufficient histogram publishing accuracy. To address this problem, we propose a symmetric histogram publishing method DPHR (differential privacy histogram released). Firstly, the algorithm uses the exponential mechanism to sort the counting of the original histogram bucket globally to improve the grouping accuracy; secondly, we propose an optimal dynamic symmetric programming grouping algorithm based on the global minimum error, which uses the global minimum error as the error evaluation function based on the ordered histogram. This way, we can achieve a global grouping of the optimal error balance while balancing the reconstruction and Laplace errors. Experiments show that this method effectively reduces the cumulative error between the published histogram and the original histogram under long-range counting queries based on satisfying \u03b5-differential privacy and improves the usability of the published histogram data.<\/jats:p>","DOI":"10.3390\/sym15051099","type":"journal-article","created":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T06:00:29Z","timestamp":1684389629000},"page":"1099","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Symmetry Histogram Publishing Method Based on Differential Privacy"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5630-2070","authenticated-orcid":false,"given":"Tao","family":"Tao","sequence":"first","affiliation":[{"name":"College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"School of Computer Science and Technology, Anhui University of Technology, Ma\u2019anshan 243032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siwen","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Anhui University of Technology, Ma\u2019anshan 243032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2022-5747","authenticated-orcid":false,"given":"Jun","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Anhui University of Technology, Ma\u2019anshan 243032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shudong","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Anhui University of Technology, Ma\u2019anshan 243032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huajun","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhou, N., Long, S., Liu, H., and Liu, H. 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