TAP: An Adjustable Planar Structure for Adaptive Topology Control in Wireless Ad Hoc Networks

In wireless ad hoc networks, a planar topology enables nodes to deliver packets without a routing table. Pervious planar structures are fixed for the whole network. However, environmental or network dynamics such as channel status, interference or 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 nodes to adjust the topology independently and allows nodes to have different path loss exponent. We show by proof or simulation properties of TAP: (1) It preserves connectivity; (2) It is planar, sparse and symmetric; (3) It preserves all minimum energy path when t=1 for all nodes; (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.