Linear Time Approximation Algorithms for the Relay Node Placement Problem in Wireless Sensor Networks with Hexagon Tessellation

Algorithm 1

The proposed approximation algorithm for the MGDC problem.

Algorithm Hexagon-I

Input: A set of points, and a two-dimensional region .

Output: A set of disks with radius that covers .

(1) Let the width of the vertical strips be and the height of the horizontal strips be , where , , and

   is the shifting parameter (a positive integer).

(2) Min-Cardinality = ; Min-Set =  // Min-Set contains the minimum number

                 // of hexagon disks that cover found so far

(3) For to do {

(4)   Set the starting position of vertical strips at

(5)   For to do {

(6)     Set the starting position of horizontal strips at

(7)     Let  // contains the chosen hexagon disks that cover points in

(8)     For each () square-like region in do

(9)       For to do { // 0 is for the case of no points in

(10)         For each combination of hexagon disks in do

(11)          Check whether the hexagon disks cover all the points in

(12)          If yes then add the hexagon disks to and break the -loop

(13)       }

(14)     If < Min-Cardinality then { Min-Set = ; Min-Cardinality =

(15)   }

(16) }

(17) Output Min-Set