Distributed memory

connected component labeling

Definition

• Given an undirected graph G = (V, E) with n = |V|, m= |E|

• purpose: Find connected component and each vertex's label

• Array of tuple<p, q, u>, notion as A(i), p and q will change in each iteration

• Bucket, notion as B(i)(p), means a tuple which first item is p

• Candidates, notion as C(i)(p), means a tuple which second item is p

• Minium candidate, motion min(p), means a tuple in candidates with minium first item

Sequential algorithm

• Init:
  for each vertex u add tuple <u, u, u>
  for each edge {u, v} add tuple <u, v, u>
  and <v, u, v>

• Each iteration
  for every p, find min(p), update all tuple <p, q> in b(i)(p) with <q, min(p)>

• Terminate statement
  The first and second item in tuple is same

Parallel algorithm

• Data Distribution                                       each process has their own A(i)/p

• Parallel sort

• Bucket update
  Find min(p), with parallel, the bucket might cross process, the code use mpi_exscan to reduce the complex from O(n) to O(logn)

Scalability

• With vertex = 100000                               np = 1,  8485(ms)
  np = 4, 5144(ms)
  np = 9, 3732(ms)
  np = 16, 4120(ms)
  np = 64, 10119(ms)

• With vertex = 1000000
  np = 1, 855927(ms)
  np = 4, 533112(ms)
  np = 9, 380247(ms)
  np = 16, 396492(ms)

TODO

• Evaluate cuda                                        

• Understand parconnect library usage