Constrained Delaunay Triangulation for Ad Hoc Networks

Algorithm 1

Algorithm for CDT

(1)  Construct PLDel, set color of each node to WHITE,

   and broadcast all its 1-hop neighbor information

   using the packet Neighbor_Packet.

(2)  Nodes having lowest id among its 2-hop neighbors set

   their color to BLACK.

(3)  Each BLACK node chooses a set 𝑁 of nodes from its

   1-hop neighbors using the following

   method, see Figure 4.

    (a) 𝑁 = empty

    (b) 𝑛₁ = farthest neighbor

    (c) 𝑁 = 𝑁∪𝑛₁

    (d) for 𝑖=2,3,…

      {

      𝑛_𝑖 = choose 𝑖th farthest neighbor

      if 𝑛_𝑖 makes more than 60^∘ angle with

      𝑛₁,𝑛₂,…,𝑛_𝑖−1

      then 𝑁 = 𝑁∪𝑛_𝑖

      }

(4)  Each BLACK node adds the constraint edges to the

   nodes in 𝑁 and broadcasts these constraint edges

   information using the message Constraint_Packet.

(5)  Each WHITE node sets its color = BROWN if it is

   other end of any constrained edges received using

   Constraint_Packet.

(6)  Each BROWN node broadcasts its constraint edge information

   using the control packet Constraint_Packet.

(7)  All WHITE and BROWN nodes remove edges connec-

   ted to it which crosses constraint edges, see Figure 5(b).

   This information is broadcasted using Edgecross_Packet.

(8)  Each BLACK node places a new edge from the WHITE

   nodes, from which the edge was deleted in the previous

   step to form new triangles, see Figure 6.