1. Dynamic Decomposition Search for the One-Eye Problem Akihiro Kishimoto kishi@cs.ualberta.ca

2. Outline Motivations Our decomposition search algorithm Current experimental results Conclusions

3. Motivation of this research Solving tsume-Go is hard –Large number of moves –Deep search to detect alive/dead Successful research on decomposition search [Mueller:IJCAI’99] –Applicable to endgames –Assume positions are already decomposed Can we apply divide and conquer approach to life and death/one-eye problems?

4. Basic Idea of Dynamic Decomposition Search Example Divide and Conquer –Try to make an eye in left or right region –Reduce branching factor and search depth Issues –How to decompose positions? –Which region must be chosen?

5. Dynamic Decomposition Search Algorithm (1 / 6) Example Undivided positions –Generate all moves

6. Dynamic Decomposition Search Algorithm (2 / 6) Divided into sub- positions by: –Attacker’s connections to safe stones –Defender’s crucial stones Example

7. Dynamic Decomposition Search Algorithm (3 / 6) Narrowing region –Defender’s choice to determine working region –Use move ordering by search algorithms Proof and disproof numbers Example

8. Dynamic Decomposition Search Algorithm (4 / 6) Attacker plays in sub- region –Reduce branching factor and search depth Example

9. Dynamic Decomposition Search Algorithm (5 / 6) Region extension –Occurs when defender plays at boundary of connections –Attacker generates all moves in extended region Example

10. Dynamic Decomposition Search Algorithm (6 / 6) Narrowing region –Region narrowed again if attacker connects –Attacker’s choice to/not to connect Move ordering by search algorithm Example

11. Current Result (1 / 5) Athlon 2800MP + 300 MB TT 140 test positions Time limit: 5minites per position # of problems solved: –With dynamic decomposition search: 137 –Without DDS :136

12. Position Solved only by Dynamic Decomposition Search White to live Look impressive?

13. Current Results (2 / 5)

14. Current Results (3 / 5)

15. Current Results (4 / 5)

16. Current Results (5 / 5)

17. Conclusions and Future Work Successfully achieved higher performance by dynamically decomposing positions? –Need more problems for fair comparison! Still room for improvement Need to consider the case of tsume-Go problem