Results 1 
2 of
2
Localized Delaunay Triangulation with Application in Ad Hoc Wireless Networks
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2003
"... Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RNG) or Gabriel graph (GG) is used as such planar structure. However, it is wellknown that the spanning ratios of these two grap ..."
Abstract

Cited by 49 (8 self)
 Add to MetaCart
Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RNG) or Gabriel graph (GG) is used as such planar structure. However, it is wellknown that the spanning ratios of these two graphs are not bounded by any constant (even for uniform randomly distributed points). Bose et al. [11] recently developed a localized routing protocol that guarantees that the distance traveled by the packets is within a constant factor of the minimum if Delaunay triangulation of all wireless nodes is used, in addition, to guarantee the delivery of the packets. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we model the network as a unitdisk graph (UDG), in which a link uv exists only if the distance kuvk is at most the maximum transmission range. In this paper, we present a novel localized networking protocol that constructs a planar 2.5spanner of UDG, called the localized Delaunay triangulation (LDEL), as network topology. It contains all edges that are both in the unitdisk graph and the Delaunay triangulation of all nodes. The total communication cost of our networking protocol is Oðn log nÞ bits, which is within a constant factor of the optimum to construct any structure in a distributed manner. Our experiments show that the delivery rates of some of the existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. Our simulations also show that the traveled distance of the packets is significantly less when the FACE routing algorithm is applied on LDEL, rather than applied on GG.
VoroNet: A scalable object network based on voronoi tessellations
 In Proceedings of the 21st International Parallel and Distributed Processing Symposium (IPDPS 2007
, 2007
"... In this paper, we propose the design of VoroNet, an objectbased peer to peer overlay network relying on Voronoi tessellations, along with its theoretical analysis and experimental evaluation. VoroNet differs from previous overlay networks in that peers are application objects themselves and get iden ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
In this paper, we propose the design of VoroNet, an objectbased peer to peer overlay network relying on Voronoi tessellations, along with its theoretical analysis and experimental evaluation. VoroNet differs from previous overlay networks in that peers are application objects themselves and get identifiers reflecting the semantics of the application instead of relying on hashing functions. This enables a scalable support for efficient search in large collections of data. In VoroNet, objects are organized in an attribute space according to a Voronoi diagram. VoroNet is inspired from the Kleinberg’s smallworld model where each peer gets connected to close neighbours and maintains an additional pointer to a longrange neighbour. VoroNet improves upon the original proposal as it deals with general object topologies and therefore copes with skewed data distributions. We show that VoroNet can be built and maintained in a fully decentralized way. The theoretical analysis of the system proves that routing in VoroNet can be achieved in a polylogarithmic number of hops in the size of the system. The analysis is fully confirmed by our experimental evaluation by simulation. 1