Neighbor-finding based on space-filling curves

Nearest neighbor-finding is one of the most important spatial operations in the field of spatial data structures concerned with proximity. Because the goal of the space-filling curves is to preserve the spatial proximity, the nearest neighbor queries can be handled by these space-filling curves. When data is ordered by the Peano curve, we can directly compute the sequence numbers of the neighboring blocks next to the query block in 8 directions in the 2D-space based on its bit shuffling property. But when data is ordered by the RBG curve or the Hilbert curve, neighbor-finding is complex. However, we observe that there is some relationship between the RBG curve and the Peano curve, as with the Hilbert curve. Therefore, in this paper, we first show the strategy based on the Peano curve for the nearest neighbor query. Next, we present the rules for transformation between the Peano curve and the other two curves, including the RBG curve and the Hilbert curve, such that we can also efficiently find the nearest neighbor by the strategies based on these two curves. From our simulation, we show that the strategy based on the Hilbert curve requires the least total time (the CPU-time and the I/O time) to process the nearest neighbor query among our three strategies, since it can provide the good clustering property. (