S.G. Akl, D.T. Barnard, and R.J. Doran, Design, analysis and implementation of a parallel tree search algorithm, IEEE Transactions on Machine Analysis and Artificial Intelligence, 4(2), 1982, 192--203.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....will sketch the concept of our parallelization of the game tree search. A detailed description including the pseudo code of an implementation can be found in [20] For many years it has been an open problem how to parallelize the game tree search and a lot of research has been done in this field [3, 25, 36, 39, 24, 37, 17, 27, 43, 26, 18, 19, 20, 21, 5, 30, 49]. Three difficulties have to be dealt with when searching subtrees in parallel. They are shown in the figure to the right as a triangle. Search overhead Work load Performance Distributed TR table YBW concept Load balancing ffl Processor work load: Since the game tree search routines use cutoffs ....

S.G. Akl, D.T. Barnard, R.J Doran Design, Analysis and Implementation of a Parallel Tree Search Algorithm IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2), pp 192--203, 1982

.... Date First Processor Parallelism Synchronization (Reference) Described Hierarchy Possible At Done At These Control These Nodes Nodes Distribution Parallel Aspiration Search 1978 Static Root (fffi window) Root (Baudet, 1978) Centralized Mandatory Work First 1979 Static Type 1 3 Left Bad Type 2 (Akl, Barnard and Doran, 1982) Centralized most child of 3 Tree Splitting 1980 Static Top k ply Root (Finkel and Fishburn, 1982) Centralized PV Split 1981 Static Type 1 Type 1 (Marsland and Campbell, 1982) Centralized Key Node 1983 Static Type 1 3 Left Bad Type 2 (Lindstrom, 1983) Centralized most child of 3 UIDPABS 1986 ....

.... June 12, 1996 Algorithm Hardware Test Sequential Trans Speedup (Reference) Used Domain Algorithm Position Obtained Table Parallel Aspiration Search Simulation Artificial fffi none 6 for large n (Baudet, 1978) Trees (simulated) Mandatory Work First Simulation Artificial fffi score 6 for large n (Akl, Barnard and Doran, 1982) Trees table (simulated) Tree Splitting LSI 11 Checkers fffi none 2.34 (n=3) Finkel and Fishburn, 1982) Simulation 5.12 (n=27,sim) PV Split Sun 3 Chess PVS local 3.75 (n=5) Marsland, Olafsson and Schaeffer, 1985) Network Key Node Simulation Artificial fffi none 12.57 (n=20) Lindstrom, 1983) ....

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Akl, S. G., Barnard, D. T., and Doran, R. J. (1982). Design, Analysis and Implementation of a Parallel Tree Search Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-4, No. 2, pp. 192--203.

....execution time, the overall efficiency inevitably drops to less than 50 . Unfortunately the paper of Frye and Myczkowski contains no other speedup measures or efficiency data. 5. 2 Adversary Games In the area of two person games, early simulation studies with a Mandatory Work First (MWF) scheme [ Akl et al. 1982 ] and the PVSplit algorithm [ Marsland and Campbell, 1982 ] showed that a high degree of parallelism was possible, despite the work imbalance introduced by pruning. Those papers recognized that in many applications, especially chess, the game trees tend to be well ordered because of the wealth ....

....] thus the bulk of the computation occurs during the search of the first subtree. The MWF approach recognizes that there is a critical tree that must be searched. Since that tree is well defined and has regular properties (see Fig. 7) it is easy to generate. In their simulation of the MWF method Akl et al. 1982 ] consider the merits of searching the critical game tree in parallel, with the balance of the tree being generated algorithmically and searched quickly by simple tree splitting. Fishburn and Finkel [ 1982 ] also favor this method and provide some analysis. The first subtree of the critical game ....

S.G. Akl, D.T. Barnard, and R.J. Doran. Design, analysis and implementation of a parallel tree search machine. IEEE Trans. on Pattern Anal. and Mach. Intell., 4(2):192-- 203, 1982.

....YBW concept Load balancing The only hope to get scalable parallelism in a game tree search is to split the game tree and search the resulting subtrees in parallel. For many years it has been an open problem how to parallelize the game tree search and a lot of research has been done in this field [7, 27, 2, 28, 44, 32, 49, 63, 26, 31, 46, 50, 51, 18, 33, 35, 55, 30, 37, 19, 21, 22, 23, 4, 38, 65]. Three difficulties have to be dealt with when searching subtrees in parallel. They are shown in the figure above as a triangle. Processor work load: Since the game tree search routines use cutoffs during the search, the size of a subtree is not known in advance. Thus, a dynamic load ....

S.G. Akl, D.T. Barnard, R.J Doran Design, Analysis and Implementation of a Parallel Tree Search Algorithm IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2), pp 192-203, 1982

....can increase the search overhead. In practice, the right balance between these sources of program inefficiency is difficult to find, and one usually performs many experiments to find the right trade offs to maximize performance. Many parallel fffi algorithms have appeared in the literature [1, 2, 3, 9, 13, 22]. The PV Split algorithm recognized that some nodes exist in the search tree where, having searched the first branch sequentially, the remaining branches can be searched in parallel [16] Initiating parallelism along the best line of play, the principal variation, was effective for a small number ....

S. G. Akl, D. T. Barnard, and R. J. Doran. Design, Analysis and Implementation of a Parallel Tree Search Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4(2):192-- 203, 1982.

.... Date First Processor Parallelism Synchronization (Reference) Described Hierarchy Possible At Done At These Control These Nodes Nodes Distribution Parallel Aspiration Search 1978 Static Root (fffi window) Root [6] Centralized Mandatory Work First 1979 Static Type 1 3 Left Root Bad Type 2 [2] Centralized most child of 3 Tree Splitting 1980 Static Top k ply Root [34] Centralized PV Split 1981 Static Type 1 Type 1 [61] Centralized Key Node 1983 Static Type 1 3 Left Root Bad Type 2 [55] Centralized most child of 3 UIDPABS 1986 Static Root None [69] Centralized DPVS 01 1987 ....

....the algorithm. 49 Algorithm Hardware Test Sequential Trans Speedup (Reference) Used Domain Algorithm Position Obtained Table Parallel Aspiration Search Simulation Artificial fffi none 6 for large n [6] Trees (simulated) Mandatory Work First Simulation Artificial fffi score 6 for large n [2] Trees table (simulated) Tree Splitting LSI 11 Checkers fffi none 2.34 (n=3) 34] Simulation 5.12 (n=27,sim) PV Split Sun 3 Chess PVS local 3.75 (n=5) 63] Network Key Node Simulation Artificial fffi none 12.57 (n=20) 55] Trees UIDPABS Data General Chess fffi local 3.94 (n=8) 69] mixed ....

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S. G. Akl, D. T. Barnard, and R. J. Doran. Design, Analysis and Implementation of a Parallel Tree Search Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4(2):192--203, 1982. (47,49,51)

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S.G. Akl, D.T. Barnard, and R.J. Doran, Design, analysis and implementation of a parallel tree search algorithm, IEEE Transactions on Machine Analysis and Artificial Intelligence, 4(2), 1982, 192--203.

....computer, with p processors, on the other hand, can search the game tree up to a depth of d p , where d p d 1 , that is examine B dp leaves in T time units. The parallel computer, therefore, makes a more informed decision when choosing its move, having looked farther ahead in the game tree [5]. 2 The situation described in the preceding example has worked fairly well for some games, such as Chess. For instance, the world Chess champion today is a parallel computer [50] There is, however, no proof that this strategy works in all cases, for at least two reasons: 1. The game tree is ....

S.G. Akl, D.T. Barnard, and R.J. Doran, Design, analysis and implementation of a parallel tree search algorithm, IEEE Transactions on Machine Analysis and Artificial Intelligence, 4(2), 1982, 192--203. 20

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S.G. Akl, D.T. Barnard, and R.J. Doran, Design, analysis and implementation of a parallel tree search algorithm, IEEE Transactions on Machine Analysis and Artificial Intelligence, 4, 1982, 192--203.

.... unit is defined in terms of the speed of the processors available (namely, the single processor on the sequential computer and each processor on the parallel machine) 2 Previous Work The fact that parallel computers can do more than just speed up computations had been suspected for some time [1, 3]. However, it was one particular paradigm, namely, real time computation, that provided the appropriate environment for this phenomenon to manifest itself for the first time. It was shown that for two computations, each from a different class of problems, a solution obtained in parallel is ....

S.G. Akl, D.T. Barnard, and R.J. Doran, Design, analysis and implementation of a parallel tree search algorithm, IEEE Transactions on Machine Analysis and Artificial Intelligence, 4, 1982, 192--203.

....computer, with p processors, on the other hand, can search the game tree up to a depth of d p , where d p d 1 , that is examine B dp leaves in time units. The parallel computer, therefore, makes a more informed decision when choosing its move, having looked farther ahead in the game tree [4]. The situation described in the preceding example has worked fairly well for some games, such as Chess. For instance, the world Chess champion today is a parallel computer [29] There is, however, no proof that this strategy works in all cases, for at least two reasons: 1. The game tree is not ....

S.G. Akl, D.T. Barnard, and R.J. Doran, Design, analysis and implementation of a parallel tree search algorithm, IEEE Transactions on Machine Analysis and Artificial Intelligence, 4, 1982, 192--203.

....was used to demonstrate that parallelism can do more than just speed up computation. It is shown in [3] that for real time optimization problems, a solution obtained in parallel can be closer to optimal than any solution computed sequentially. Another example is provided by game playing programs [2, 23]. Consider, for instance, a program for playing chess in real time (against a human or another program) Suppose that the program runs on a parallel computer and that it is its turn to make a move. Given a fixed amount of time to move, the program can search a game tree much larger than is ....

S.G. Akl, D.T. Barnard, and R.J. Doran, Design, analysis and implementation of a parallel tree search algorithm, IEEE Transactions on Machine Analysis and Artificial Intelligence, 4, 1982, 192--203.

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S.G. Akl, D.T. Barnard, R.J Doran Design, Analysis and Implementation of a Parallel Tree Search Algorithm IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 4 No. 2, pp 192-203, (1982)

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