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Once all nodes in the network have an initial location, a relaxation algorithm is run to improve the convexity of the network. This is only run once and uses a spring method. Nodes share relaxation packets enabling them to learn of their one-hop neighbours and any shared neighbours. Note that reference node p1 does not participate in the relaxation phase so that it has a constant location at the origin which all nodes in the network is aware of.

Node's Self-Information One-Hop Neighbours
Stable Bit Node ID X-Coord Y-Coord Z-Coord Node ID Node ID Node ID ...
Table: Relaxation Packet Structure (TYPE_PSVC, APP_RELAX)

Node ID X-Coord Y-Coord Z-Coord Stable Bit Two-Hop TTL
Table: Neighbour List Structure

Nodes first broadcast their own information and will only add to their one-hop neighbour table after receiving other nodes' relaxation packets. A list of two-hop neighbours from each node is also maintained. The stable bit informs whether the node has converged to a stable location yet and is merely periodically broadcasting its coordinates.

For relaxation, each node (defined as node i) compares itself against each of its neighbours (defined as node j) individually. The percentage of neighbours which node i and node j share is defined as rij, and is used to calculate the rest length of the spring between node i and j. Force exerted on the spring is then calculated and the net force on a node determines its new position.

[EQ. 5, 6, 7, 8 and variable definitions]

[Parameters used] -- XiaohongWu - 2012-01-24

Topic revision: r3 - 2012-01-25 - XiaohongWu
 
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