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SSS* and Dual*

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<span id="RecSSS"></span>
=RecSSS* and RecDual*=
The development of [[Recursion|recursive]] variants was driven by the need for a better understanding of '''SSS'''*'s node expansion process and by the demand for more efficient implementations. Two recursive variants were proposed 1990: '''RecSSS'''* <ref>[[Subir Bhattacharya]], [[Amitava Bagchi]] ('''1990'''). ''Unified Recursive Schemes for Search in Game Trees.'' Technical Report WPS-144, [https://en.wikipedia.org/wiki/Indian_Institute_of_Management_Calcutta Indian Institute of Management, Calcutta]</ref> by [[Subir Bhattacharya]] and [[Amitava Bagchi]] and '''SSS-2''' <ref>[[Wim Pijls]], [[Arie de Bruin]] ('''1990'''). ''Another View on the SSS* Algorithm.'' . International Symposium SIGAL '90 (eds. T. Asano, T. Ibaraki, H. Imai, and T. Nishizeki), pp. 211-220. Tokyo, Japan. Lecture Notes in Computer Science, Vol. 450, Springer-Verlag, New York, NY. ISSN 0302-9743.</ref> by [[Wim Pijls]] and [[Arie de Bruin]]. In 1993 [[Alexander Reinefeld]] improved '''RecSSS'''*, making it both faster and more space efficient, using an OPEN-[[Array|array]] rather than dynamic list structures <ref>[[Alexander Reinefeld]] ('''1994'''). ''A Minimax Algorithm Faster than Alpha-Beta''. [[Advances in Computer Chess 7]]</ref> .
==Pseudo C-Code==
<span id="SSStarandDualStarAsMT"></span>
=SSS* and Dual* as MT=
[[Aske Plaat]], [[Jonathan Schaeffer]], [[Wim Pijls]] and [[Arie de Bruin]] proved with their Memory Test framework, that both '''SSS'''* and '''Dual'''* can be reformulated as a sequence of [[Alpha-Beta|alpha-beta]] [[Null Window|null window]] calls with a [[Transposition Table]] <ref>[[Aske Plaat]], [[Jonathan Schaeffer]], [[Wim Pijls]], [[Arie de Bruin]] ('''19951994, 2014'''). ''SSS* = Alpha-Beta + TT'' Technical Report EUR. TR-CS-9594-0217, [[University of Alberta]], [httphttps://publishing.eurarxiv.nlorg/irabs/repub/asset/1441/eur-few-cs-95-021404.1517 arXiv:1404.pdf pdf1517]</ref> :
==Pseudo C-Code==
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At the [[Advances in Computer Chess 8|8th Advances in Computer Chess]] conference 1996, '''SSS'''* was finally declared "dead" by [[Wim Pijls]] and [[Arie de Bruin]] <ref>[[Arie de Bruin]], [[Wim Pijls]] ('''1997'''). ''SSS†.'' [[Advances in Computer Chess 8]]</ref> <ref>[[Aske Plaat]], [[Jonathan Schaeffer]], [[Wim Pijls]], [[Arie de Bruin]]('''1996'''). ''Best-First Fixed-Depth Minimax Algorithms.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 87, Nos. 1-2, [http://www.ldc.usb.ve/%7Ebonet/courses/ci5437/papers/mtd.pdf pdf]</ref> .
=See also=
* [[Subir Bhattacharya]], [[Amitava Bagchi]] ('''1990'''). ''Unified Recursive Schemes for Search in Game Trees.'' Technical Report WPS-144, [https://en.wikipedia.org/wiki/Indian_Institute_of_Management_Calcutta Indian Institute of Management, Calcutta]
* [[Hans-Joachim Kraas]] ('''1990''').''Zur Parallelisierung des SSS*-Algorithmus''. Ph.D thesis, [https://en.wikipedia.org/wiki/Technical_University_of_Braunschweig TU Braunschweig] (German)
* [[Wim Pijls]], [[Arie de Bruin]] ('''1990'''). ''Another View on the SSS* Algorithm.'' International Symposium SIGAL '90 (eds. T. Asano, T. Ibaraki, H. Imai, and T. Nishizeki), pp. 211-220. Tokyo, Japan. Lecture Notes in Computer Science, Vol. 450, Springer-Verlag, New York, NY. ISSN 0302-9743.
* [[Claude G. Diderich]] ('''1992'''). ''Evaluation des performance de l'algorithme SSS* avec phases de synchronisation sur une machine parallèle à mémoires distribées''. Technical report LITH-99, [https://en.wikipedia.org/wiki/%C3%89cole_Polytechnique_F%C3%A9d%C3%A9rale_de_Lausanne Swiss Federal Institute of Technology], Computer Science Theory Laboratory, Lausanne, Switzerland (French)
* [[Alexander Reinefeld]] ('''1994'''). ''A Minimax Algorithm Faster than Alpha-Beta''. [[Advances in Computer Chess 7]]
* [[Aske Plaat]], [[Jonathan Schaeffer]], [[Wim Pijls]], [[Arie de Bruin]] ('''1994, 2014'''). ''[http://arxiv.org/abs/1404.1517?context=cs.AI SSS* = aAlpha-b Beta + TT]''. TR-CS-94-17, [[University of Alberta]], [https://arxiv.org/abs/1404.1517 arXiv:1404.1517]
* [[Alexander Reinefeld]], [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/r/Ridinger:Peter.html Peter Ridinger] ('''1994'''). ''[http://www.sciencedirect.com/science/article/pii/0004370294900493 Time-Efficient State Space Search]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 71, No. 2, [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.1934 CiteSeerX]
* [[Aske Plaat]], [[Jonathan Schaeffer]], [[Wim Pijls]], [[Arie de Bruin]] ('''1996'''). ''An Algorithm Faster than NegaScout and SSS* in Practice'', . [http://citeseerx.ist.psu.edu/showciting;jsessionidviewdoc/download?doi=04E25D5F074D8B5BABB68D2AC5BA5D39?cid10.1.1.77.9111&rep=rep1&type=3161130 pdf pdf] from [httphttps://citeseerxen.ist.psuwikipedia.eduorg/viewdocwiki/summary?doi=10.1.1.50.8641 CiteSeerX CiteSeerX], covers » [[MTD(f)]]
* [[Arie de Bruin]], [[Wim Pijls]] ('''1997'''). ''SSS†.'' [[Advances in Computer Chess 8]]
==2000 ...==* [[Aske Plaat]], [[Arie de Bruin]], [[Jonathan Schaeffer]], [[Wim Pijls]] ('''19992003'''). ''A Minimax Algorithm better than SSS*[https://repub.eur.nl/pub/459 Trends in game tree search]'' . [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial IntelligenceErasmus_University_Rotterdam Erasmus University, Rotterdam], Vol. 87
==2010 ...==
* [[Bojun Huang]] ('''2015'''). ''[https://www.semanticscholar.org/paper/Pruning-Game-Tree-by-Rollouts-Huang/a38b358745067f71a9c780db117ae2471e693d63 Pruning Game Tree by Rollouts]''. [[AAAI]] » [[SSS* and Dual*#SSStarandDualStarAsMT|MT-SSS*]], [[Monte-Carlo Tree Search|MCTS]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=66280&start=67 Re: Announcing lczero] by [[Daniel Shawul]], [[CCC]], January 21, 2018 » [[Leela Chess Zero]]</ref>

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