Abstract
In wireless ad hoc networks, the constructed topology is preferred to be planar since a planar topology enables guaranteed delivery of packets without a routing table. Previous planar structures are statically constructed for the whole network. However, environmental or network dynamics such as channel status, interference, or residual energy will prevent such structures from providing the best service to the network. In this paper, we present a t-adjustable planar structure (TAP) which enables each node to adjust the topology independently via a parameter t and allows nodes to have different path loss exponent. TAP is based on three well-known planar structures: Gabriel Graph, Relative Neighborhood Graph, and Local Minimum Spanning Tree. We show properties of TAP by proof or simulation: (1) It preserves connectivity; (2) it is planar, sparse, and symmetric; (3) it preserves all minimum energy path when t = 1 for all nodes; and (4) the average transmission power, interference, and node degree decrease as t increases and the maximum node degree is bounded by 6 when t = 3 for all nodes.
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