Shortest Paths Based Web Service Selection in Internet of Things

Algorithm 5

PruningBFSKNN(𝐺,𝐶,𝑘,𝑠).

Input: A (weighted) graph 𝐺=(𝑉,𝐸), candidate set 𝐶, 𝑘 nearest neighbors, and source node 𝑠;

Output: A list 𝑙 of (𝑛𝑜𝑑𝑒,𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒) from 𝑠, where |𝑙|≤𝑘;

(1) let 𝑅=𝑛𝑢𝑙𝑙;

(2) let 𝑅^′={𝑣_𝑖,𝑐𝐿𝑖𝑠𝑡_𝑖,𝑑_𝑖∣𝑣_𝑖==𝑠?0∶+∞,𝑐𝐿𝑖𝑠𝑡_𝑖=0,0≤𝑖≤|𝐺|};

(3)  while  𝑅^′≠𝑅  do

(4)  𝑅=𝑅^′;

(5)  PruningBFSMapper(𝑅,𝐺);

(6)  𝑅^′ = PruningBFSReducer();

(7)  end while;

(8) /*******************************************

(9) Here we redefine “∩” as follows:

(10) 𝑅∩𝐶={𝑣_𝑖,𝑑_𝑖∣(𝑣_𝑖,𝑐𝐿𝑖𝑠𝑡_𝑖,𝑑_𝑖)∈𝑅 and 𝑣_𝑖∈𝐶}

(11) *******************************************/

(12) 𝑙=𝐶∩𝑅;

(13) return  𝑙