Controlled Conspiracy-Number Search

In this paper we present a new conspiracy number search algorithm (CNS), called Controlled Conspiracy Number Search (CCNS). The basic steps of any CNS algorithm, the selection, the expansion, and the backup of results have been modiied compared to other CNS algorithms. The selection is done by assigning demands, so called CN targets, to the nodes of the tree in a top-down fashion. By this, a set of leaves is selected in a single selection phase. The expansion is used to check, whether or not a leaf node can fullll its demand. The backup uses heuristic information gained from the expansion step to prepare the tree for the next selection phase. As a result, our algorithm is stronger than the-algorithm in tactical positions. This is shown by comparing them on a set of test positions. It is able to play even in nontactical positions, as shown on the 4:IPC 3 ; where Ulysses CCN, a program based on the CCNS algorithm, played a complete tournament. In addition, since in every selection step a set of leaves is selected for expansion, the algorithm may be well suited for parallelization.

[1]  Reinhard Selten,et al.  Game Equilibrium Models III , 1991 .

[2]  Rainer Feldmaus,et al.  Spielbaumsuche mit massiv parallelen Systemen , 1993 .

[3]  Christian Donninger,et al.  Null Move and Deep Search , 1993, J. Int. Comput. Games Assoc..

[4]  Oliver Vornberger,et al.  Distributed Game-Tree Search , 1989, J. Int. Comput. Games Assoc..

[5]  K. Thompson,et al.  BELLE: chess hardware , 1988 .

[6]  Jonathan Schaeffer,et al.  The History Heuristic and Alpha-Beta Search Enhancements in Practice , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Jean-Christophe Weill The ABDADA Distributed Minimax-Search Algorithm , 1996, J. Int. Comput. Games Assoc..

[8]  Donald E. Knuth,et al.  The Solution for the Branching Factor of the Alpha-Beta Pruning Algorithm , 1981, ICALP.

[9]  Jonathan Schaeffer,et al.  Multiprocessor tree-search experiments , 1986 .

[10]  Peter Mysliwietz Konstruktion und Optimierung von Bewertungsfunktionen beim Schach , 1994 .

[11]  I. D. Hill,et al.  Faster than Thought. A Symposium on Digital Computing Machines , 1972 .

[12]  Jonathan Schaeffer,et al.  Kasparov versus Deep Blue: The Rematch , 1997, J. Int. Comput. Games Assoc..

[13]  Murray Campbell,et al.  Singular Extensions: Adding Selectivity to Brute-Force Searching , 1990, Artif. Intell..

[14]  Jonathan Schaeffer The History Heuristic , 1983, J. Int. Comput. Games Assoc..

[15]  Bradley C. Kuszmaul,et al.  Cilk: an efficient multithreaded runtime system , 1995, PPOPP '95.

[16]  Judea Pearl,et al.  On the Nature of Pathology in Game Searching , 1983, Artif. Intell..

[17]  David A. McAllester Conspiracy Numbers for Min-Max Search , 1988, Artif. Intell..

[18]  Aviezri S. Fraenkel,et al.  Combinatorial Games: selected Bibliography with a Succinct Gourmet Introduction , 2012 .

[19]  Yasser Seirawan The Kasparov - Deep Blue Games , 1996, J. Int. Comput. Games Assoc..

[20]  Anne-Kathrin Lauer Literaturverzeichnis. , 1935, Die Nichtangriffsverpflichtung im deutschen und europäischen Kartellrecht.

[21]  Thomas Ottmann,et al.  Data Structures and Efficient Algorithms, Final Report on the DFG Special Joint Initiative , 1992, Data Structures and Efficient Algorithm.

[22]  Maarten van der Meulen Conspiracy-Number Search , 1990, J. Int. Comput. Games Assoc..

[23]  Richard E. Korf,et al.  Distributed Tree Search and Its Application to Alpha-Beta Pruning , 1988, AAAI.

[24]  Rainer Feldmann Spielbaumsuche mit massiv parallelen Systemen , 1993 .

[25]  Vladimir L. Arlazarov,et al.  Algorithms for games , 1987 .

[26]  Bruce W. Suter,et al.  A parallel alpha/beta tree searching algorithm , 1989, Parallel Comput..

[27]  Rainer Feldmann Fail High Reductions , 1996 .

[28]  Alexander Reinefeld,et al.  Spielbaum-Suchverfahren , 1989, Informatik-Fachberichte.

[29]  Gerard Maurice Baudet,et al.  The design and analysis of algorithms for asynchronous multiprocessors. , 1978 .

[30]  Hans J. Berliner,et al.  The B* Tree Search Algorithm: A Best-First Proof Procedure , 1979, Artif. Intell..

[31]  G Schrüfer,et al.  Presence and absence of pathology on game trees , 1986 .

[32]  Ralph Udo Gasser,et al.  Harnessing computational resources for efficient exhaustive search , 1995 .

[33]  Dana S. Nau,et al.  Quality of decision versus depth of search on game trees , 1979 .

[34]  T. Anthony Marsland,et al.  Parallel Search of Strongly Ordered Game Trees , 1982, CSUR.

[35]  E. W. Felten,et al.  Chess on a hypercube , 1988, C3P.

[36]  Monty Newborn,et al.  Unsynchronized Iteratively Deepening Parallel Alpha-Beta Search , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  Warren D. Smith,et al.  A Test Suite for Chess Programs , 1993, J. Int. Comput. Games Assoc..

[38]  Rainer Feldmann,et al.  Game Tree Search on Massively Parallel Systems , 1993 .

[39]  John P. Fishburn,et al.  Parallelism in Alpha-Beta Search , 1982, Artif. Intell..

[40]  A. Reinefeld A Minimax Algorithm Faster than Alpha - Beta , 1994 .

[41]  Claude E. Shannon,et al.  Programming a computer for playing chess , 1950 .

[42]  L. V. Allis,et al.  Searching for solutions in games and artificial intelligence , 1994 .

[43]  Dana S. Nau,et al.  An Investigation of the Causes of Pathology in Games , 1982, Artif. Intell..

[44]  Murray Campbell,et al.  Singular Extensions: Adding Selectivity to Brute-Force Searching , 1990, Artif. Intell..

[45]  A. J. Palay Searching with probabilities , 1985 .

[46]  Ronald L. Rivest,et al.  Game Tree Searching by Min/Max Approximation , 1987, Artif. Intell..

[47]  Ingo Althöfer,et al.  Root Evaluation Errors: How they Arise and Propagate , 1988, J. Int. Comput. Games Assoc..

[48]  Jonathan Schaeffer,et al.  Low Overhead Alternatives to SSS , 1987, Artif. Intell..

[49]  H. Jaap van den Herik,et al.  Proof-Number Search , 1994, Artif. Intell..

[50]  J. Neumann,et al.  The Theory of Games and Economic Behaviour , 1944 .

[51]  Judea Pearl,et al.  Heuristics : intelligent search strategies for computer problem solving , 1984 .

[52]  Dap Hartmann,et al.  How Computers Play Chess , 1991, J. Int. Comput. Games Assoc..

[53]  H. J. van den Herik,et al.  A knowledge-based approach to connect-four: The game is over: White to move wins! , 1989 .

[54]  I. Bratko,et al.  Error Analysis of the Minimax Principle , 1982 .

[55]  George C. Stockman,et al.  A Minimax Algorithm Better than Alpha-Beta? , 1979, Artif. Intell..

[56]  E. Berlekamp,et al.  Winning Ways for Your Mathematical Plays , 1983 .

[57]  Jonathan Schaeffer,et al.  Conspiracy Numbers , 1990, Artif. Intell..

[58]  Jonathan Schaeffer,et al.  Distributed Game-Tree Searching , 1989, J. Parallel Distributed Comput..

[59]  D. F. Beal,et al.  BENEFITS OF MINIMAX SEARCH , 1982 .

[60]  Konrad Zuse,et al.  Der Computer-Mein Lebenswerk , 1993 .

[61]  Frederic Friedel,et al.  Pentium Genius Beats Kasparov: A Report on the Intel Speed Chess Grand Prix in London , 1994, J. Int. Comput. Games Assoc..

[62]  Feng-hsiung Hsu Large scale parallelization of alpha-beta search: an algorithmic and architectural study , 1989 .

[63]  Thomas S. Anantharaman,et al.  Extension Heuristics , 1991, J. Int. Comput. Games Assoc..