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'''Igor Steinberg''',<br/>
an American computer scientist, [https://en.wikipedia.org/wiki/Solution_architecture solution architect], teacher, and [https://en.wikipedia.org/wiki/Program_management program manager], with director-level [https://en.wikipedia.org/wiki/Information_technology IT] [https://en.wikipedia.org/wiki/Senior_management executive] experience in the higher education, government, and private sector <ref>[https://www.linkedin.com/in/igor-steinberg-89294136/ Igor Steinberg | LinkedIn]</ref>. He holds a Ph.D. from [https://en.wikipedia.org/wiki/University_of_Wisconsin-Madison University of Wisconsin-Madison] in 1991 on the topic of [[Parallel Search|parallel game tree search]] <ref>[[Igor Steinberg]] ('''1991'''). ''Design and Analysis of Parallel Algorithms for Game-Tree Search''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Wisconsin-Madison University of Wisconsin-Madison]</ref>,
and researched and published along with his thesis advisor [[Marvin Solomon]] on a parallel game tree search algorithm dubbed ER (Evaluate and Refute) algorithm.
=Algorithm ER Algorithm===Abstract==''Abstractof Searching Game Trees in Parallel'' <ref>[[Igor Steinberg]], [[Marvin Solomon]] ('''1989'''). ''Searching Game Trees in Parallel''. [https://en.wikipedia.org/wiki/University_of_Wisconsin-Madison University of Wisconsin-Madison], Technical report 877, [ftp://ftp.cs.wisc.edu/pub/techreports/1989/TR877.pdf pdf], [https://pdfs.semanticscholar.org/0814/076db01c0e5e110ef2f40539857c8e8fccd6.pdf pdf]</ref>
We present a new parallel game-tree search algorithm. Our approach classifies a processor's available work as either mandatory (necessary for the solution) or speculative (may be necessary for the solution). Due to the nature of parallel game tree search, it is not possible to keep all processors busy with mandatory work. Our algorithm ER allows potential speculative work to be dynamically ordered, thereby reducing starvation without incurring an equivalent increase in speculative loss. Measurements of ER's performance on both random trees and trees from an actual game show that at least 16 processors can be applied profitably to a single search. These results contrast with previously published studies, which report a rapid drop-off of efficiency as the number of processors increases.
==Pseudo Code==[[Negamax]] [[Cpp|C++]] like pseudo code implementation of the serial algorithm ER:<pre>struct Node { int val; bool done; vector<Node> childs;}; int er(Node& p, int α, int β) { p.val = α; p.childs = generatedChilds(p); int d = p.childs.size(); if (d ==0 ) return staticEval(p); for (int i=0; i < d; ++i) { int t = -evalFirst(p.childs[i], -β, -p.val); if (p.childs[i].done) { p.val = max (t, p.val); if (p.val >= β) return p.val; } } sort(p.childs); for (int i=0; i < d; ++i) { if (!p.childs[i].done) { int t = -refuteRest(p.childs[i], -β, -p.val); p.val = max (t, p.val); if (p.val >= β) return p.val; } } return p.val;} int evalFirst(Node& p, int α, int β) { p.val = α; p.childs = generatedChilds(p); int d = p.childs.size(); if (d ==0 ) { p.done = true; return staticEval(p); } else { int t = -er(p.childs[0], -β, -p.val); p.val = max (t, p.val); p.done = (p.val >= β) || d == 1; } return p.val;} int refuteRest(Node p, int α, int β) { p.val = α; int d = p.childs.size(); // childs already generated in evalFirst for (int i=1; i < d; ++i) { int t = -evalFirst(p.childs[i], -β, -p.val); if (!p.childs[i].done) t = -refuteRest(p.childs[i], -β, -p.val); p.val = max (t, p.val); if (p.val >= β) return p.val; } return p.val;}</pre>
=Selected Publications=
<ref>[http://dblp.uni-trier.de/pers/hd/s/Steinberg:Igor.html dblp: Igor Steinberg]</ref>
