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A Memory Efficient Retrograde Algorithm and Its Application To Chinese Chess Endgames

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. Outline. Introduction

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A Memory Efficient Retrograde Algorithm and Its Application To Chinese Chess Endgames

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  1. A Memory Efficient Retrograde Algorithm andIts 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. 90n 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

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