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 are ordered by the Peano curve, we can directly compute the sequence numbers of the neighboring blocks next to the query block in eight directions in the 2D-space based on its bit shuffling property. But when data are ordered by the RBG curve or the Hilbert curve, neighborfinding 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 nearestneighbor 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. r
In a structured P2P system, peers maintain information about what resources neighbor peers offer. Chord is one of well-known structured P2P systems to efficiently support resource finding based on the hashing approach. However, in Chord, most of data keys may be assigned to the same peer, since it uses the static hashing scheme, resulting in the case that the load of Chord is unbalanced. Therefore, we propose a strategy which uses the dynamic hashing scheme to locate the data key based on the Chord architecture, and to maintain the load balance. From our simulation results, we show that the load of the P2P system based on our strategy is much more balanced than that based on the original strategy used in Chord.
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