Research Article
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 |
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