Distributive Generation Algorithm of Long Range Contact for Remote Spatial-data Access on P2P Delaunay Network

A P2P Delaunay network is a network that connects nodes over 2-dimensional plane by utilizing a well-known geometric structure, a Delaunay triangulation in computational geographically geometry. This structure possesses the property that two adjacent nodes are connected. We have shown its autonomous generation algorithm in P2P settings with a greedy routing among two arbitrary nodes, and also shown the extensibility of the network. By setting Voronoi regions as a node´s governing a area, a P2P Delaunay network works as a spatial database, and we can easily embed a range query mechanism over the network, realizing a extensible spatial database in P2P contexts. We aim at the diverse applications in geographical information systems (GIS), virtual collaboration systems, location-aware services, and so on. However, in case a P2P Delaunay network consists of a large number of nodes, its diameter and hop counts between two nodes increase in O(N^1/2), which causes a serious communication delay in remote data accesses. Hence, we here propose long range contact(LRC) for a P2P Delaunay network and its distributive generation algorithm. Our LRC is a set of bridges that connect two nodes in O(logN) hops with O(logN) node degree. We present a combination of horizontal/vertical generation algorithm in a collaboration of autonomous nodes, as well as a routing methods that utilizes LRC. We also evaluate both CPU and communication loads in our LRC generation, as well as routing efficiencies of LRC numerically. Finally, we discuss application fields of a P2P Delaunay network with LRC.