Efficient and Scalable Graph Similarity Joins in MapReduce

Algorithm 4

Replacement of verification of Algorithm 1.

(1) Map   ⟨𝑟𝑖𝑑,𝑟⟩/⟨𝑟𝑖𝑑,𝑠𝑖𝑑⟩⟨𝑠𝑖𝑑,𝑠⟩

(2)   if   ⟨𝑟𝑖𝑑,𝑟⟩   then   emit(⟨(ℎ(𝑟𝑖𝑑),𝑥),⟨𝑟𝑖𝑑,𝑟⟩⟩) for any 𝑥   if   ⟨𝑟𝑖𝑑,𝑠𝑖𝑑⟩   then

    emit(⟨(ℎ(𝑟𝑖𝑑),ℎ(𝑠𝑖𝑑)),⟨𝑟𝑖𝑑,𝑠⟩⟩), for any 𝑦  else   emit𝑦,ℎ(𝑠𝑖𝑑),⟨𝑠𝑖𝑑,𝑠⟩

(3) Reduce   ⟨(ℎ(𝑟𝑖𝑑),ℎ(𝑠𝑖𝑑)),𝑙𝑖𝑠𝑡(𝑣𝑎𝑙𝑢𝑒)⟩→⟨𝑟𝑖𝑑,𝑠𝑖𝑑⟩

(4)  split 𝑙𝑖𝑠𝑡(𝑣𝑎𝑙𝑢𝑒) into 𝑙𝑖𝑠𝑡(⟨𝑟𝑖𝑑,𝑟⟩),𝑙𝑖𝑠𝑡(⟨𝑠𝑖𝑑,𝑠⟩) and 𝑙𝑖𝑠𝑡(⟨𝑟𝑖𝑑,𝑠𝑖𝑑⟩);

(5)  denote 𝑙𝑖𝑠𝑡(⟨𝑟𝑖𝑑,𝑠𝑖𝑑⟩) as joinkey;

(6)  for   ⟨𝑟𝑖𝑑,𝑠𝑖𝑑⟩∈𝑗𝑜𝑖𝑛𝑘𝑒𝑦𝑠,𝑤ℎ𝑒𝑟𝑒⟨𝑟𝑖𝑑,𝑟⟩∈𝑙𝑖𝑠𝑡(⟨𝑟𝑖𝑑,𝑟⟩)𝑎𝑛𝑑⟨𝑠𝑖𝑑,𝑠⟩∈𝑙𝑖𝑠𝑡(⟨𝑠𝑖𝑑,𝑠⟩)   do

(7)     if   𝑔𝑟𝑎𝑝ℎ𝑠  𝑟𝑎𝑛𝑑𝑠𝑖𝑛⟨𝑟,𝑠⟩𝑎𝑟𝑒𝑣𝑒𝑟𝑦𝑙𝑎𝑟𝑔𝑒  then invoke MRGED

     calculation else invoke the A^∗-based in-memory algorithm