Cs403 Parellel Programming Travelling Salesman Problem
- 1. CS403 : Parellel Programming Travelling Salesman Problem Design of Parallel Algorithm
- 2. Team Members ● P Jishnu Jaykumar (201352005) ○ 201352005@iiitvadodara.ac.in ● Vivek Kumar Singh (201352015) ○ 201352015@iiitvadodara.ac.in ● Rahul Nalawade (201351017) ○ 201351017@iiitvadodara.ac.in ● Ajay Shewale (201351030) ○ 201351030@iiitvadodara.ac.in
- 3. Table of contents ● Possible ways to parallelize. ● Describing strategies with task graphs and algorithms. ● Analyzing strategies with speed-up calculations
- 4. Possible ways to parellelize NOTE : We are only designing two ways to parellelize our serial code.
- 5. Serial algorithm Input : Adjacency matrix containing cost value between two cities. Output : Optimal Hamiltonian circuit with minimum travel cost. Procedure : ● Calculate all possible travel routes (more specifically circuits). ○ i.e. Permutation of all possible travel path ● Calculate total cost corresponding to each travel route. ● Pick the route with minimum travel cost ○ This would be the optimal Hamiltonian path. ○ The travel path corresponding to this travel cost will be the output.
- 6. First Approach : Parallel Design Input : Adjacency matrix containing cost value between two cities. Output : Optimal Hamiltonian circuit with minimum travel cost. Procedure : ● Calculate all possible travel routes (more specifically circuits). ○ i.e. Permutation of all possible travel path -- This would run sequentially one after the other. ● Divide permutations among various threads. ○ Let there be n! permutated paths and p processors. ○ Each processor will have (n!/p) travel paths. -- Let us call this travel chunk. ● Each processor will calculate total cost corresponding to each travel route in the travel chunk. ● Pick the route with minimum travel cost in each travel chunk. ○ This would be the sub-optimal Hamiltonian path ● After calculation of all the minimum travel paths from each travel chunk, ● pick out the minimal cost travel path out of this filtered list. ○ The travel path corresponding to this travel cost will be the output.
- 7. Task Graph
- 8. Speed-up calculations ● Speed up is based on ideal conditions. ● Speed up = T_serial / T_parellel ● Theoretically ○ T_parellel = T_serial / n ○ Where n = number of processors ● So Speed up = n ● Graphs will be provided once parallel algorithms are coded.
- 9. Second Approach ( Using Shared Space & mutex) Input : Adjacency matrix containing cost value between two cities. Output : Optimal Hamiltonian circuit with minimum travel cost. Procedure : Shared Variable → Min Cost=infinity (theoretically) & Min Circuit. ● Calculate all possible travel routes (more specifically circuits). ● Divide permutations among various threads. ○ Let there be n! permutated paths and p processors . ● In each thread, while adding each edge from the permutation list, check if total cost after adding it is greater than Min Cost. If Yes, drop that permutation, no need of further calculation. Start calculation for other permutation from the list.
- 10. Second Approach ( Using Shared Space & mutex) ● If the minimum cost of the permutation is less than Min Cost. Then Update the value of the Min Cost and Update the value of MinCircuit with that permutation cost and permutation. ● All threads will update the MinCost shared variable and MinCircuit . ● At the end, We finally get Minimum Cost and Minimum Circuit.
- 11. Task Graph
- 12. Speed-up calculations ● Speed up is based on ideal conditions. ● Speed up = T_serial / T_parellel ● Theoretically ○ T_parellel = ((T_serial / n) - X) ○ Where n = number of processors ○ X= number of cities with no edge between them. ● So Speed up = (n / (1 - (n*X / T_serial))) ● Graphs will be provided once parallel algorithms are coded.
- 13. Any Queries?
- 14. Thank you ...