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Vincenzo Auletta, Sajal K. Das, Amelia De Vivo, M. Cristina Pinotti, Vittorio Scarano, "Optimal Tree Access by Elementary and Composite Templates in Parallel Memory Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 13, no. 4, pp. 399412, April, 2002.  
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@article{ 10.1109/71.995820, author = {Vincenzo Auletta and Sajal K. Das and Amelia De Vivo and M. Cristina Pinotti and Vittorio Scarano}, title = {Optimal Tree Access by Elementary and Composite Templates in Parallel Memory Systems}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {13}, number = {4}, issn = {10459219}, year = {2002}, pages = {399412}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.995820}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Optimal Tree Access by Elementary and Composite Templates in Parallel Memory Systems IS  4 SN  10459219 SP399 EP412 EPD  399412 A1  Vincenzo Auletta, A1  Sajal K. Das, A1  Amelia De Vivo, A1  M. Cristina Pinotti, A1  Vittorio Scarano, PY  2002 KW  complete trees KW  composite templates KW  conflictfree access KW  elementary templates KW  mapping scheme KW  parallel memory system VL  13 JA  IEEE Transactions on Parallel and Distributed Systems ER   
In this paper, we study efficient strategies for mapping onto parallel memory systems complete trees that are accessed by fixed templates (like complete subtrees, paths, or any combinations their of). These mappings are evaluated with respect to the following criteria: 1) the largest number of data items that can be accessed in parallel without memory conflicts; 2) the number of memory conflicts that can occur when accessing templates of size equal to the number of available memory modules, thereby exploiting the full parallelism of the system; 3) the complexity of the memory addressing scheme, i.e., the cost of retrieving the module where a given data item is mapped. We show that there exist tradeoffs between these three criteria and the performance of different mapping strategies depends on the emphasis given on each of these criteria. More specifically, we describe an algorithm for mapping complete binary trees of height H onto M memory modules and prove that it achieves the following performance results: 1) conflictfree access to complete subtrees of size K and paths of size N such that N+K\lceil\log K\rceil \leq M; 2) at most 1 conflict in accessing complete subtrees and paths of size M; 3) O\left({K\over M} + c\right) conflicts when accessing a composite template of K nodes consisting of c disjoint subsets, each subset being a complete subtree, or a path or a set of consecutive nodes in a level of the tree. Furthermore, we show that an existing mapping algorithm results in a larger number, namely O\left({K\over{\sqrt{M\log M}}} + c\right), of conflicts when accessing a composite template. However, such an algorithm maps each single node in O(1) time, while the new algorithm requires O(H/N\log K) time.
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