## 1 Introduction
[PERSON] and [PERSON] [PERSON] and [PERSON] (2018) decomposed map coordinates based on discrete wavelet decomposition and then embedded watermarks into low-frequency coefficients with the retrieval of watermarked vector data using inverse wavelet transformation. [PERSON] et al. [PERSON] et al. (2018) proposed a reversible watermarking algorithm for vector maps based on the discrete cosine transform. As there are high correlations among vertices belonging to the same polygon in a vector map, the algorithm performs the discrete cosine transform on individual data block composed of every eight vertices and embeds watermark in the cosine change coefficients. Vector map watermarking algorithms based on both the coordinate domain and the frequency domain directly operate the coordinate points. Even if changes to the original map data are controlled within given ranges, errors are inevitably introduced for subsequent analysis and thus the overall accuracies of the vector maps are reduced. In addition, to control the map accuracies, the watermark capacities of both the coordinate-domain and frequency-domain algorithms are relatively small. Reversible watermarking and zero-watermarking developed in recent years are two popular watermarking algorithms that have zero-disturbance characteristics. Reversible watermarking of vector maps is an extension of the coordinate domain algorithm. The watermark message is embedded in the least significant bit by the difference between two adjacent points. When the copyright information is verified, the watermark is extracted according to the rule of judging the difference between two points and the original data are then restored after extraction [PERSON] et al. (2018). The reversible watermarking technique embeds the watermark information in all vertices and therefore it allows for increasing the watermark capacity, and as a result, scholars have developed various large-capacity reversible watermarking schemes [PERSON] et al. (2018); [PERSON] et al. (2018); [PERSON] et al. (2018). Because reversible watermarking completely removes watermark information from the embedded data after data restoration, meaning that the watermarking can be used only once, the approach does not satisfy the user demand for permanent watermarking. Zero-watermarkingcould overcome the drawback by constructing watermarks based on feature information of digital data and storing watermarking information in the authoritative third-party protection center [37]. Because zero-watermarking does not directly embed watermarks in digital data, it does not alter the original data and thus possesses the advantages of zero-disturbance. Zero-watermarking has already been applied to various data types [38; 39; 40] and offers opportunities for the applications in vector maps with high fidelity. There are pioneer studies on zero-watermarking of vector maps and most of them mainly focus on the mining and construction of stable feature information [41; 42; 43]. The zero-watermarking of a vector map often has the problems of small watermark capacity and lack of robustness because of complex types of attacks to vector maps and the limitation posed by the stability and distribution of feature information. The idea of multiple-watermarking [44; 45] that integrates multiple algorithms to embed watermarks based on diverse requirements in different embedding domains [46] can theoretically overcome these shortcomings. Compared to the individual watermarking scheme, multiple-watermarking is more functional and robust to attacks as well as increasing the watermark capacity. Note that multiple-watermarking typically alters the original data greatly and multiple-watermarking based on the zero-watermarking scheme could perfectly avoid influencing the original data. Designing a dual zero-watermarking scheme for vector maps with large capacity and multi-attack resistance could offer an effective watermarking method to meet the application needs.