Implementation  of  Dijsktra’s  Algorithm  

in  Parallel Meenakshi Muthuraman #5009 7719

Priyanka Kulkarni #5009 8043

Single  Source  Shortest  Path  Problem

• The Problem of finding the shortest path from a source vertex  S to all vertices in the graph • Weighted graph G = (V,E)

Dijkstra’s  Algorithm •  Solution to single source shortest path algorithm in graph theory

o Both directed and undirected graphs o All edges must have non-negative weights o Graph must be connected o Dijkstra’s algorithm runs in O(E*lg|V|)

Pseudo  code  of  Dijkstra’s  Algorithm  

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Serial  Execution  Time

100 1000 5000 10000 15000 20000 25000 27000 Execution  time 0 0.02 0.74 3.3 7.94 13.58 21.64 25.16

Serial  Execution  time

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MPI  ExecutionTime  as  the  Number  of  Nodes  increases 1node*4tasks  per  node 2nodes*4tasks  per  node 3nodes*4tasks  per  node

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EXEC

UTION  TIM

E MPI  Execution  Time  as  The  Number  of  Tasks  per  node  is  Increased    

3nodes*4tasks  per  node 3nodes*8tasks  per  node

 

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SpeedUP  MPI  2*4

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168 244

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Execution  Time  for  Hadoop 2nodes*4tasks  per  node 3nodes*4tasks  per  node

Conclusions  and  Deductions •  Generating the random graphs was a challenge •  MPI outperformed the serial and Hadoop •  MPI is the winner !!

Thank  You    

Any  Questions?