Research Article
Linear Time Approximation Algorithms for the Relay Node Placement Problem in Wireless Sensor Networks with Hexagon Tessellation
Algorithm 2
A simple linear time approximation algorithm for the MGDC problem.
Algorithm Hexagon-II | Input: A set of points, and a two-dimensional region . | Output: A set of disks with radius that covers . | Step 1: | Virtually tessellate the region with hexagons of length . Calculate and store the coordinate of the center and | the corresponding index of each hexagon in the tessellation. (Each index contains two ranks (_rank, _rank) | to -axis and -axis, respectively, as shown in Figure 5.) | Step 2: | For each point with Cartesian coordinate (, ) in do | (1) ; // find the indices of the basic rectangle that contains | If _rank is even | | else | | (2) Find the hexagon containing by comparing the distances from to the centers of hexagons with indices | (_rank, _rank), (_rank + 1, _rank), and (_rank + 1, _rank + 1) if _rank is even or (_rank + 1, _rank − 1) | if _rank is odd. Ties are broken in favor of the marked hexagon, otherwise broken arbitrary. | (3) Mark the hexagon chosen in (2). | Step 3: | Output the circumscribed circles of the chosen hexagons. |
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