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<p><b>Abstract</b>—Nodes in a hexagonal network are placed at the vertices of a regular triangular tessellation, so that each node has up to six neighbors. The network is proposed as an alternative interconnection network to mesh connected computer (with nodes serving as processors) and is used also to model cellular networks where nodes are base stations. In this paper, we propose a suitable addressing scheme for nodes (with two variants), derive a formula for distance between nodes, and present a very simple and elegant routing algorithm. This addressing scheme and corresponding routing algorithm for hexagonal interconnection are considerably simpler than previously proposed solutions. We then apply the addressing scheme for solving two problems in cellular networks. With the new scheme, the distance between the new and old cell to which a mobile phone user is connected can be easily determined and coded with three integers, one of them being zero. Further, in order to minimize the wireless cost of tracking mobile users, we propose hexagonal cell identification codes containing three, four, or six bits, respectively, to implement a distance based tracking strategy. These schemes do not have errors in determining cell distance in existing hexagonal based cellular networks, which is not the case with recently proposed 3 bit cell identification codes based on an artificial square mesh placed over a hexagonal network (moreover, the existing mesh schemes fail to address the diagonal moves that may cause additional unrecoverable errors). Our schemes provide efficient implementation of distance and movement based tracking schemes in cellular networks, by providing information generally not available to the user, and means to manipulate it for accurate cell distance determination. Another application is for connection rerouting in cellular networks during a path extension process. In a path extension scheme, the path for ongoing calls is extended from the old base station to a new one using the link between neighboring base stations. If the path is extended several times due to mobility, our scheme provides an elegant way to reroute the connection from the latest base station to the base station of original connection and, therefore, minimize the length of extended path.</p>
Cellular networks, hexagonal networks, routing, location management.

F. G. Nocetti, I. Stojmenovic and J. Zhang, "Addressing and Routing in Hexagonal Networks with Applications for Tracking Mobile Users and Connection Rerouting in Cellular Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 13, no. , pp. 963-971, 2002.
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