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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

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

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

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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

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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

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Algorithm ：

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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. )

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90 n is too large, n is the number of pieces

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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

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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.)

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Table 4 ：

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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.

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aegp-aaee ：

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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

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