Forming a Convex Polygon of Mobile Sensors

Abstract

Forming a convex polygon of a plurality of mobile sensors in an area is provided. Sensor output data received from the plurality of mobile sensors in the area is analyzed using an optimization problem. It is determined whether the plurality of mobile sensors forms the convex polygon in the area. In response to determining that the plurality of mobile sensors does form the convex polygon in the area, an objective function and a set of constraints corresponding to the optimization problem are generated. Then, a sparse solution of the optimization problem is calculated using the objective function and the set of constraints to determine vector weight values for each of the plurality of mobile sensors.

What is claimed is: 
     
         1 . A computer implemented method for forming a convex polygon of a plurality of mobile sensors in an area, the computer implemented method comprising:
 analyzing, by a computer, sensor output data received from the plurality of mobile sensors in the area using an optimization problem;   determining, by the computer, whether the plurality of mobile sensors forms the convex polygon in the area;   responsive to the computer determining that the plurality of mobile sensors does form the convex polygon in the area, generating, by the computer, an objective function and a set of constraints corresponding to the optimization problem; and   calculating, by the computer, a sparse solution of the optimization problem using the objective function and the set of constraints to determine vector weight values for each of the plurality of mobile sensors.   
     
     
         2 . The computer implemented method of  claim 1  further comprising:
 determining, by the computer, whether there are mobile sensors in the plurality of mobile sensors with a vector weight value below a vector weight threshold value; 
 responsive to the computer determining that there are mobile sensors in the plurality of mobile sensors with a vector weight value below a vector weight threshold value, removing, by the computer, those mobile sensors in the plurality of mobile sensors that have a vector weight value below the vector weight threshold value from the convex polygon. 
 
     
     
         3 . The computer implemented method of  claim 2  further comprising:
 responsive to the computer determining that there are no mobile sensors in the plurality of mobile sensors with a vector weight value below the vector weight threshold value, resetting, by the computer, the vector weight threshold value. 
 
     
     
         4 . The computer implemented method of  claim 3 , wherein the computer resets the vector weight threshold value by increasing the vector weight threshold value to increase the statistical significance of received sensor output data. 
     
     
         5 . The computer implemented method of  claim 1  further comprising:
 adding, by the computer, new mobile sensors in a neighborhood of the convex polygon that have a vector weight value above the vector weight threshold value to the convex polygon. 
 
     
     
         6 . The computer implemented method of  claim 1  further comprising:
 generating, by the computer, the convex polygon using a set of mobile sensors in the plurality of mobile sensors. 
 
     
     
         7 . The computer implemented method of  claim 1  further comprising:
 associating, by the computer, labels with the sensor output data received from the plurality of mobile sensors that form the convex polygon over the area, wherein the labels describe a type of data being measured by the plurality of mobile sensors. 
 
     
     
         8 . The computer implemented method of  claim 7  further comprising:
 matching, by the computer, the labels associated with the sensor output data received from the plurality of mobile sensors that form the convex polygon with prototype data, wherein the prototype data describes a current status of the area. 
 
     
     
         9 . The computer implemented method of  claim 8 , further comprising:
 analyzing, by the computer, the sensor output data received from the plurality of mobile sensors that form the convex polygon based on the prototype data corresponding to the matching labels to determine the current status of the area associated with the convex polygon.   
     
     
         10 . The computer implemented method of  claim 9 , further comprising:
 determining, by the computer, an action to perform based on the current status of the area associated with the convex polygon.   
     
     
         11 . The computer implemented method of  claim 1 , wherein the computer receives the sensor output data from the plurality of mobile sensors in the area via a wireless network. 
     
     
         12 . The computer implemented method of  claim 1 , wherein each of the plurality of mobile sensors is free to move in any direction and independently of other mobile sensors in the plurality of mobile sensors. 
     
     
         13 . The computer implemented method of  claim 1 , wherein the objective function is a difference between a vector associated with prototype data that describes a current status of the area and a sum of vector weight values associated with the plurality of mobile sensors that represent the sensor output data. 
     
     
         14 . The computer implemented method of  claim 1 , wherein the sensor output data is time dependent. 
     
     
         15 . The computer implemented method of  claim 1 , wherein the sensor output data corresponding to the area is represented as a set of vector weight values that are defined by solving the optimization problem over the convex polygon. 
     
     
         16 . The computer implemented method of  claim 1 , wherein each of the plurality of mobile sensors is located in a mobile client device. 
     
     
         17 . The computer implemented method of  claim 16 , wherein the mobile client device that includes a set of sensors is a vehicle. 
     
     
         18 . The computer implemented method of  claim 16 , wherein the mobile client device that includes a set of sensors is a wireless communication device. 
     
     
         19 . The computer implemented method of  claim 1 , wherein the set of constraints is a set of conditions that the sparse solution of the optimization problem is required to satisfy. 
     
     
         20 . The computer implemented method of  claim 1 , wherein at least one of a size and a shape of the convex polygon changes over a period of time.