1. Knight’s Tour Distributed Problem Solving Knight’s Tour Yoav Kasorla Izhaq Shohat

2. Agenda Introduction and Motivation Possible approaches Preliminary research results

3. Aim The aim of the project is to find the optimal distribution of the knight Tour problem over a given number of processors.

4. Knights Tour – constraints

5. Knights Tour – constraints (contd.) Observe Propagator A knight can jump to one of the 8 possible squares (maximum) on a chess board, from its current position. Similarly, for reaching this current position, it could have come from one of the 8 possible positions. 8 being the maximum possible number of options and 2 being the minimum.

6. Tree Search Solution found

7. Background Constraint Satisfaction Problem (CSP) is, “Finite set of variables taking integer values with a set of constraints that limit the set of values these variables can take.” The Task The task is to find one or all solutions. How? Constraint based tree search.

8. Problem.... Combinatorial Explosion The size of the tree grows exponentially with the problems size. Concern This makes solving relatively small problems difficult.

9. Solution.... Search parallelization through distribution. Network of computers can be used for solving “search path problem”, by distributing part of the search tree to computers over the network. What would it achieve? Provide more computational resources (memory and processor). Expedite the search process. And would result in better utilization of the network resources.

10. Possible Approaches Embarrassingly parallel – distributing the problem into 8 big separate parallel problems, with no communication at all. 133 23 323 33/3 33

11. Possible Approaches Master Slave – master performs a fix depth recursion stages (according to serial research) and send the board to slaves for continuing exploration in parallel. 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

12. Possible Approaches Dynamic Spawn Manager Client Monitor Client Clients  request the manager for task  explore subtree  send updates to manager (solutions or path to explored sub trees) Manager  initializes the search space  finds work for client when requested  collects updates from client and update manager tree

13. Experimentation (contd.) Experimentation - (contd.) The experimentation was split into two parts. The first part will be estimating number of nodes in the search tree and, the second part will be estimating the time required by the search engine to explore a fixed number of nodes. Assuming network latency to be negligible (as compared to the time required for exploration of subtrees), the results can be assumed to be same for the distributed setup.

14. Experimentation – the unbalanced tree

15. Thank You Thank You Any questions ?