Conspiracy Number Search

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Conspiracy Number Search, (CNS, cns) a best-first search algorithm first described by David McAllester based on Conspiracy Numbers of the root. Trees are grown in memory - in an often deep and narrow way - that maximizes the conspiracy required to change the root value. The phases of the best-first search procedure are Selection of a leaf node, Expansion and Evaluation of that leaf, and to Back-up the result of that evaluation back to the root.

=CNS= CNS maintains a range of possible values and keeps expanding the tree until a certain degree of confidence is reached. The confidence is measured by the width of a possible values’ range W and a minimum value for conspiracy numbers T. The purpose of the search is to raise the conspiracy numbers of unlikely values to greater than T in order to reduce the range of possible values to below W. At each turn, CNS tries to disprove either the highest or lowest possible value, which has the highest  conspiracy numbers, by expanding one of its conspirators. Then, it recalculates conspiracy numbers and repeats the process until the desired confidence is obtained. Since W depends on the number of possible evaluation values, fine grained evaluation, considered necessary for good positional play, yields into additional computation and thus inefficient search. Further, a final alpha-beta quiescence search in early CNS implementations was quite expensive due to the lack of bounds. =CCNS= Ulf Lorenz' and Valentin Rottmann's et al. proposed improvements dubbed Controlled Conspiracy Number Search (CCNS) address the drawbacks of CNS by introducing general CN Targets and Extended Conspiracy Numbers. CN targets (security demands) are splitted over the successors in order to inform each node about the goal of its examination. Extended Conspiracy Numbers of the root are defined as the least number of leaf nodes that must change their value in order to change the decision at the root to another move. =PCCNS= Parallel Controlled Conspiracy Number Search (PCCNS) aims at a dynamic distribution of the game tree, initiating a worker/employer relationship along with a sophisticated splitting heuristic of CN targets. The stack, used to keep the nodes of the best-first search, could be manipulated from outside in order to share work and integrate results from other processors.

=See also=
 * Alpha-Beta Conspiracy Search
 * Conspiracy Numbers
 * Proof-Number Search

=Chess Programs= performing CNS or its improvements:
 * Arachne (CNS)
 * P.ConNerS (PCCNS)
 * Ulysses (CCNS)

=Publications=

1985 ...

 * David McAllester (1985). A New Procedure for Growing Minimax Trees. Technical Report, Artificial Intelligence Laboratory, MIT
 * David McAllester (1988). Conspiracy Numbers for Min-Max Search. Artificial Intelligence, Vol. 35, No. 1
 * Ingo Althöfer (1988). Root Evaluation Errors: How they Arise and Propagate. ICCA Journal, Vol. 11, Nos. 2/3
 * Maarten van der Meulen (1988). Parallel Conspiracy-Number Search. M.Sc. thesis, Faculty of Mathematics and Computer Science, Vrije Universteit, Amsterdam
 * Norbert Klingbeil (1988). Search Strategies for Conspiracy Numbers. M.Sc. thesis
 * Norbert Klingbeil, Jonathan Schaeffer (1988). Search Strategies for Conspiracy Numbers. Canadian Artificial Intelligence Conference, pp. 133-139
 * Jonathan Schaeffer (1989). Conspiracy Numbers. Advances in Computer Chess 5 » also published in AI
 * Charles Elkan (1989). Conspiracy Numbers and Caching for Searching And/Or Trees and Theorem-Proving. IJCAI 1989, pdf

1990 ...

 * Maarten van der Meulen (1990). Conspiracy-Number Search. ICCA Journal, Vol. 13, No. 1
 * Norbert Klingbeil, Jonathan Schaeffer (1990). Empirical Results with Conspiracy Numbers. Computational Intelligence, Vol. 6
 * Jonathan Schaeffer (1990). Conspiracy Numbers. Artificial Intelligence, Vol. 43, No. 1
 * Maarten van der Meulen, Victor Allis, Jaap van den Herik (1990). A Comment on `Conspiracy-Number Search`. ICCA Journal, Vol. 13, No. 2
 * Victor Allis, Maarten van der Meulen, Jaap van den Herik (1991). Conspiracy-Number Search. Advances in Computer Chess 6
 * David McAllester, Deniz Yuret (1993). Alpha-Beta Conspiracy Search. ps (draft)
 * Lisa Lister, Jonathan Schaeffer (1994). An Analysis of the Conspiracy Numbers Algorithm. Computers & Mathematics with Applications Vol. 27, No. 1, Elsevier, pdf
 * Deniz Yuret (1994). The Principle of Pressure in Chess. TAINN 1994

1995 ...

 * Ulf Lorenz, Valentin Rottmann, Rainer Feldmann, Peter Mysliwietz (1995). Controlled Conspiracy-Number Search. ICCA Journal, Vol. 18, No. 3
 * Ulf Lorenz, Valentin Rottmann (1996). Parallel Controlled Conspiracy-Number Search. Advances in Computer Chess 8
 * Ulf Lorenz (1999). Controlled Conspiracy-2 Search. Technical Report, Paderborn University
 * Robin Upton (1999). Dynamic Stochastic Control - A New Approach to Game Tree Searching. Ph.D. thesis, University of Warwick

2000 ...

 * Ulf Lorenz (2000). Controlled Conspiracy Number Search. Paderborn University, Dissertation, advisor Burkhard Monien (German)
 * Ulf Lorenz (2000). Controlled Conspiracy-2 Search. Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS)
 * David McAllester, Deniz Yuret (2002). Alpha-Beta Conspiracy Search. ICGA Journal, Vol. 25, No. 1
 * Ulf Lorenz (2002). Parallel Controlled Conspiracy Number Search. Euro-Par 2002, LNCS 2400, Springer

2010 ...

 * Mohd Nor Akmal Khalid, Umi Kalsom Yusof, Hiroyuki Iida, Taichi Ishitobi (2015). Critical Position Identification in Games and Its Application to Speculative Play. ICAART 2015
 * Mohd Nor Akmal Khalid, E. Mei Ang, Umi Kalsom Yusof, Hiroyuki Iida, Taichi Ishitobi (2015). Identifying Critical Positions Based on Conspiracy Numbers. Agents and Artificial Intelligence, ICAART 2015 - Revised Selected Papers
 * Jakub Pawlewicz, Ryan Hayward (2015). Sibling Conspiracy Number Search. SoCS 2015
 * Jakub Pawlewicz, Ryan Hayward (2016). Conspiracy number search with relative sibling scores. Theoretical Computer Science, Vol. 644
 * Quang Vu, Taichi Ishitobi, Jean-Christophe Terrillon, Hiroyuki Iida (2016). Using Conspiracy Numbers for Improving Move Selection in Minimax Game-Tree Search. ICAART 2016, pdf
 * Zhang Song, Hiroyuki Iida (2018). Using single conspiracy number for long term position evaluation. CG 2018, ICGA Journal, Vol. 40, No. 3

=External Links=
 * Conspiracy from Wikipedia
 * Conspiracy (disambiguation) from Wikipedia
 * Conspiracy (board game) from Wikipedia
 * Jeanne Lee - Sundance, Conspiracy (1975), YouTube Video
 * feat.: Jack Gregg, Mark Whitecage, Steve McCall, Gunter Hampel, Sam Rivers, Marty Cook

=References= Up one level