1. A Memory Efficient Retrograde Algorithm and Its Application To Chinese Chess Endgames  Reference ： MSRI Publications Volume 42, 2002  Writer ： Ren Wu. Department of Computer Science, Queen Mary & Westfield College  Reporter ： 梁秦宜

2. Outline  Introduction  Fast, Memory Efficient Retrograde Algorithm  Reducing the Size of the Database  Results from the Database  Conclusion

3. Introduction  Endgame databases have several benefits.  Goal --- new retrograde algorithm and reducing the size of the database  Previous Work --- retrograde with burst force

4. Fast, Memory Efficient Retrograde Algorithm  Previous ： 帥、炮、兵 vs 將、象 帥、兵 vs 將、象帥、炮 vs 將、象帥、炮、兵 vs 將 帥、兵 vs 將帥 vs 將、象帥、炮 vs 將 帥 vs 將

5.  New ： difference 1. use only one bit per position to generate full information for both sides 2. generate a pair databases, one for each side  Example ： construct a 5-men pawn-less chess endgame database, 15MB RAM is sufficient to avoid random disc access

6.  Algorithm ：

7. Reducing the Size of the Database  Limiting the Pieces' Placement to Legal Squares. ( Table 1. )  Vertical Symmetry. ( Table 2. )  Multiple Piece Symmetry. ( Table 3. )  Piece Grouping. ( Table 3. )

8.  90 n is too large, n is the number of pieces

9.  Table3 ： 1. there is more than one piece of the same type, we can exchange these pieces' places without altering the position 2. consider a few different type of pieces together  maximum savings is incorporating the symmetry reduction

10. Results from the Database  One Major Piece.  One Major Piece Plus a Pawn.  Two Major Pieces.  One Gunner, One Pawn Plus Some Minor Pieces.  Two Gunners Plus Some Minor Pieces.  Two Pawns Plus One Major Piece.  Some of the Hard Subgames. ( Table 4.)

11.  Table 4 ：

12.  Special case ： The aegp-aaee Endgame  Human Analyses ： Draw Game! 1.Shi Qin Ya Qu 2.Pao Bin Endgames the aeegp-aaee endgame is theory win for the stronger side  Use 95 moves to capture the first piece, and prove the Pao Bin Endgames theory.

13.  aegp-aaee ：

14. Conclusion  improved, memory efficient retrograde algorithm  prove that the aegp-aaee is a winning endgame, which maximum number of moves the stronger side need to capture the first piece is 95