Shortest Paths Based Web Service Selection in Internet of Things

Algorithm 1

DijkstraKNN(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={(𝑠,0)};

(2) let 𝑅.𝑁𝑂𝐷𝐸={𝑟.𝑛𝑜𝑑𝑒∣𝑟∈𝑅};

(3) /*******************************************

(4) Here we redefine “∩” as follows:

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

(6) *******************************************/

(7)  while |𝑅∩𝐶|<𝑘∧∃(𝑢,𝑣)(𝑢∈𝑅.𝑁𝑂𝐷𝐸∧𝑣∈(𝑉(𝐺)−𝑅.𝑁𝑂𝐷𝐸)∧(𝑢,𝑣)∈𝐸(𝐺))  do

(8)  DijkstraMapper(𝑅,𝐺);

(9)  //find a nearest neighbour

(10)  𝑅=𝑅  ∪ DijkstraReducer();

(11)  end while

(12)  𝑙=𝐶∩𝑅;

(13)  return  𝑙