1. Recent Progress on the One-eye Solver Akihiro Kishimoto kishi@cs.ualberta.ca

2. Outline of this Talk Previous Status of my Research Techniques Recently Added Experimental Results Conclusions Future Work

3. Previous Progress Built a high performance one-eye solver –Depth-first proof-number search –Minimal distance heuristics –Connections to safe/crucial stones –Forced moves –Simulation

4. Recent Progress Methods recently implemented –Heuristic initialization for proof and disproof numbers –Elimination of useless moves Preliminary for a divide-and-conquer approach

5. Heuristic Initializations Basic proof-number search variants –If (n is a leaf node) n.pn = n.dn = 1 Proof-number search with heuristic initializations (e.g. [Allis:94] [Breuker et al.:94][Nagai:99]) –If (n is a leaf node) { n.pn = EstimateProofNumber(n); n.dn = EstimateDisproofNumber(n) }

6. Current Implementation for Heuristic Initializations Definitions: –Proof cannot make the second eye # of eye spaces is used for estimating pn –Disproof can make the second eye Distance to an eye is used for estimating dn Note: Initializations to proof and disproof numbers are combined with the move generator Df-pn looks up all the information on children

7. Examples Distance to an eye# of eye spaces 2 2 55 44 4 81 1 2 2 2 23 3

8. One Issue on Heuristic Initializations Higher overhead for re-expanding interior nodes 15 Basic df-pndf-pn + initialization 11 Leaf 55 th.pn=2 th.pn=6 pn OR node pn AND node

9. Solution to the Overhead of the Re-expansion Compute an average evaluation value of all the children Use that number as a unit to the threshold Example 5 56 Leaf 7 th.pn = 6 + (5 + 6 + 7) / 3 = 6 + 6 = 12 pn OR node pn AND node

10. Experimental Results for Heuristic Initializations For 136 test positions solved (Athlon 2400MP 200 MB TT) Total nodes Time Node / sec. df-pn without init 18,197,651 456 39,907 df-pn + dn init 15,135,326 359 42,159 df-pn + pn & dn init 9,015,558 189 47,701

11. Eliminating Useless Moves Preliminary stage for a divide-and-conquer approach Divide-and-Conquer Approach

12. Eliminating Useless Move (cont’d) Algorithm –Compute connections to safe stones using the miai strategy –Detect regions divided by safe stones considering connections –Don’t generate moves in the regions that do not have potential eye spaces Example

13. Experimental Results: Useless Move Elimination For 136 problems solved Total nodes Time Node / sec. df-pn without init 18,197,651 456 39,907 df-pn + dn init 15,135,326 359 42,159 df-pn + pn & dn init 9,015,558 189 47,701 df-pn + init + move elim. 7,725,253 167 46,259

14. Conclusions and Future Work Summary –Achieving better results is always good Future work –Of course, we want more!