Tham khảo tài liệu 'current trends and challenges in rfid part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 380 Current Trends and Challenges in RFID than shift but some cases may be opposite. Therefore combining the rotation and shift can be more effective than applying any single one of them independently. 3. Spatial range query algorithms In this section we provide a theoretical analysis on the first observation and then derive a formula to measure the improvement of applying multiple copies of Hilbert curves with different orientations. We also introduce a new spatial range query algorithm designed based on the combination of rotations and shift. Theoretical proofs In this section formulas will be derived to calculate the average number of clusters for a given query region in the top and bottom boundary of a 2 -oriented Hilbert curve. And then we prove that the average number of clusters within given query region on 2--oriented Hilbert curve is smaller than the average number of clusters on 2 -oriented Hilbert curve when the queries are located on the bottom boundary of the space. This proof can be extended to queries located in other areas and Hilbert curves with other orientations. Specifically we assume that the query window is a region with size 2k 2k and the size of the grid space is 2k n 2k n. The notations used in the proof are listed in Table 1. We define connection edge in a 2k n 2k n Hilbert curve as the edge that connects two sub curves each with size 2k 2k. Fig. 4. Hk n divided into 9 subregions. The grid space of Hk n is divided into nine sub regions as shown in Fig. 4. The smaller side length of each sub region on the boundary is 2k. Then the 2k n 2k n grid region Hk n can be considered as a collection of 22n Hk each of which connects to one or two neighbors by connection edges. The following proves are deducted from parts of the conclusions in Moon et al. 2001 . By definition of Hilbert curve 2 -oriented Hilbert curve and 2--oriented Hilbert curve are symmetrical when given the curve-space order so for given query region the average number of .
