1. Search for Transitive Connections Ling Zhao University of Alberta October 27, 2003 Author: T. Cazenave and B. Helmstetter published in JCIS'03

2. Motivations Goal: find double connections Potential problems: - Search complexity global search vs. local search b 2d vs. 2b d ABC

3. Examples (white plays first) AB C ABC Transitive connectionNon-transitive connection

4. Basic ideas - Search Search for each connection separately, and send back a trace (set of intersections) that may change the result. Results: - yes: two strings connected - no: one of the two strings is captured in a ladder - unknown otherwise

5. Generalized Threats Search Not mandatory Order of a threat: number of moves in a row the max player has to play to win the game Finding possible moves that connect in one move, in two moves, or in three moves

6. Framework Search connection C1 and C2 separately when max player moves first, then search C1 and C2 when min player is first. If it is max player to move: Lost if: C1 or C2 is lost when max player plays first Win if: one of connection is win (even if min plays first), and the other is winnable (win if max plays first) and the traces the results depend on are disjoint. win lost

7. If no results found Change to a global search: alphabeta + TT + killer moves + history heuristic Reuse previous search results: moves for min player: union of traces moves for max player: moves of order up to the order of maximum threat + 1

8. Experimental Results 21 problems: a half from classic problems, and the other half from computer Go games GTS limited to 4000 nodes Max moves: order up to 3 19 solved, 2 unsolved due to limited moves searched and no ko handling

9. Examples Machine used: 1.7 GHz CPU + 100Mb RAM A B C 6523413 nodes, 33.190 sec

10. Conclusions Effective to search for double connections Incomplete (results can be wrong) Too slow sometimes but can be further optimized Future work: extend it to a more general search problem for combining sub-goals