## 1 Introduction  
In the era of digitalization today, concerns about the privacy and security of user-sensitive data coexist with the progression of data mining technologies. These privacy apprehensions can surface at every phase of the data mining and analysis procedure, encompassing data collection, data publication, data transmission, and data analysis. Recently, there has been extensive research [1; 2; 3] aimed at effectively mitigating privacy threats to sensitive information during data mining and analysis, with significant contributions, including differential privacy techniques [4; 5; 6]. Differential privacy is a privacy-preserving paradigm defined from a probabilistic statistical standpoint [4; 5; 6]. In the context of database queries, it involves adding noise drawn from a certain probability distribution to query results, such that the maximum impact on the result caused by either deleting (or inserting) a single record or modifying the value of a single record is confined within a predetermined range. This ensures that an attacker, with a certain probability, cannot infer whether a particular record exists or determine its true value from the query output, thereby providing privacy protection for the presence or magnitude of each individual record's information [6]. Due to its rigorous quantification of privacy guarantees and independence from an attacker's background knowledge, differential privacy is well-suited for safeguarding privacy in big data scenarios [6]. Differential privacy (DP) is considered as a de facto standard privacy definition and is applied to many privacy protection scenarios [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20], where the histogram [21] is a very typical one. The histogram adopts a box-division technology, which divides a database table into disjoint areas according to one or more column attributes and expresses each area with some statistical values to understand the distribution of various types of data. Therein, one statistical value of one disjoint area is called a bin. The histogram can be used for population census, road condition information, disease detection, product testing, daily personal activities including living expenses, web browsing, and APP statistics, etc. However, if an original histogram is directly used for publishing, it may face the problem of personal privacy leakage. For example, a hospital carries out a statistical analysis on the disease types of patients who come to the hospital this month, among whom three patients are found to have diabetes. If the number of patients with other disease types and the fact that two patients have diabetes is known, the third diabetic patient can be easily speculated. Therefore, before publishing the histogram, privacy protection is needed. In DP histogram publishing, deleting a record or adding a record to a database table has one count that affects the publication, and its sensitivity is very small. Therefore, DP histogram publishing is of great concern in the research of DP [21]. However, the uneven distribution of the original data leads to the presence of variously sized statistics (bins) in histograms constructed from the data. When bins of varying sizes comply with \(\epsilon\)-differential privacy, it is often observed that small bins exhibit lower relative accuracy compared to larger bins, sometimes to a significantly greater extent. In the relevant literature concerning the publication of differentially private histograms [13; 14; 15], the majority of studies overlook the issue of relatively lower accuracy in small bins under non-uniform data distributions. While some studies have indeed taken note of data skewness, their focus remains confined to the overall accuracy of all bins or predominantly larger bins, occasionally sacrificing the accuracy of small bins to marginally enhance the absolute accuracy of the aggregate or larger bins. Indeed, it is a well-established principle that the equitable analysis of data yields more dependable outcomes.