Monitoring Moving Queries inside a Safe Region

Algorithm 1

Extended Safe Region algorithm.

(1)   /*𝑞: query point and 𝑒: the Euclidean distance threshold */

(2)   Compute the range search of 𝑞 and store the objects of interest in the result list

(3)   Order the result list in ascending order

(4)   for all   𝑝𝑖   do

(5)    if   MINDIST𝑝1,𝑝𝑖>2𝑒   then

(6)     prune 𝑝𝑖

(7)    else

(8)     add 𝑝𝑖 to the safe-object list

(9)    end if

(10)  end for

(11)  Surround any object in the safe-object list by a circle with radius 𝑒

(12)  The area formed by overlapping regions containing 𝑞 is the Extended Safe Region of the

   range moving query

(13)  Calculate the area of the safe region using Monte-Carlo Integration.

(14)  To find when and where the query will leave the safe region, use linear motion function

   method