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Erschienen in:
2011 | OriginalPaper | Buchkapitel
k th Order Geometric Spanners for Wireless Ad Hoc Networks
verfasst von : Prabhat Kiran, S. V. Rao
Erschienen in: Distributed Computing and Internet Technology
Verlag: Springer Berlin Heidelberg
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Wireless ad hoc network can be modeled as a
unit disk graph
(UDG) in which there is an edge between two nodes if and only if their Euclidean distance is at most one unit. The size of UDG is in
O
(
n
2
), where
n
is the number of network nodes. In the literature, the geometric spanners like Relative Neighborhood Graph (RNG), Gabriel Graph (GG), Delaunay Triangulation (Del), Planarized Localized Delaunay Triangulation (PLDel) and Yao Graph are proposed, which are sparse subgraphs of UDG. In this paper, we propose a hierarchy of geometric spanners called the
k
th
order RNG (
k
-RNG),
k
th
order GG (
k
-GG),
k
th
order Del (
k
-Del), and
k
th
order Yao (
k
-Yao) to reduce the spanning ratio and control topology, sparseness and connectivity. We have simulated these spanners and compared with the existing spanners. The simulation results show that the proposed spanners have better properties in terms of spanning ratio and connectivity by controlling topology and sparseness.