TY - GEN

T1 - A new proof-number calculation technique for proof-number search

AU - Yoshizoe, Kazuki

PY - 2008

Y1 - 2008

N2 - We propose a new simple calculation technique for proof numbers in Proof-Number Search. Search algorithms based on (dis)proof numbers are known to be effective for solving problems such as tsumego, tsume-shogi, and checkers. Usually, the Proof-Number Search expands child nodes with the smallest (dis)proof number because such nodes are expected to be the easiest to (dis)prove the node. However, when many unpromising child nodes exist, (dis)proof numbers are not always a suitable measure for move ordering because unpromising nodes temporarily increase the (dis)proof numbers. For such cases, we propose the use of only some child nodes (instead of all child nodes) for calculating (dis)proof numbers. We call this technique Dynamic Widening. We combined Dynamic Widening with the Depth-first Proof-Number Search (df-pn) algorithm and tested its performance on capturing problems of Go on 19×19 boards. Our results show that the approach is more than 30 times faster than normal df-pn when we generate almost all legal moves (about 300 moves on average). The required time for processing remained approximately four times as long as that of df-pn using heuristic pruning (about 20 moves on average), but the correctness of the search result is guaranteed.

AB - We propose a new simple calculation technique for proof numbers in Proof-Number Search. Search algorithms based on (dis)proof numbers are known to be effective for solving problems such as tsumego, tsume-shogi, and checkers. Usually, the Proof-Number Search expands child nodes with the smallest (dis)proof number because such nodes are expected to be the easiest to (dis)prove the node. However, when many unpromising child nodes exist, (dis)proof numbers are not always a suitable measure for move ordering because unpromising nodes temporarily increase the (dis)proof numbers. For such cases, we propose the use of only some child nodes (instead of all child nodes) for calculating (dis)proof numbers. We call this technique Dynamic Widening. We combined Dynamic Widening with the Depth-first Proof-Number Search (df-pn) algorithm and tested its performance on capturing problems of Go on 19×19 boards. Our results show that the approach is more than 30 times faster than normal df-pn when we generate almost all legal moves (about 300 moves on average). The required time for processing remained approximately four times as long as that of df-pn using heuristic pruning (about 20 moves on average), but the correctness of the search result is guaranteed.

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U2 - 10.1007/978-3-540-87608-3_13

DO - 10.1007/978-3-540-87608-3_13

M3 - Conference contribution

AN - SCOPUS:55249084426

SN - 3540876073

SN - 9783540876076

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 135

EP - 145

BT - Computers and Games - 6th International Conference, CG 2008, Proceedings

T2 - 6th International Conference on Computers and Games, CG 2008

Y2 - 29 September 2008 through 1 October 2008

ER -