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Bounded-Collision Memory-Mapping Schemes for Data Structures with Applications to Parallel Memories
July 2007 (vol. 18 no. 7)
pp. 973-982

Abstract—Techniques are developed for mapping structured data to an ensemble of parallel memory modules in a way that limits the number of conflicts, i.e., simultaneous accesses by distinct processors to the same memory module. The techniques determine, for any given conflict tolerancec, the smallest ensemble that allows one to store anyn{\hbox{-}}\rm node data structure "of type X” in such a way that no more than c nodes of a structure are stored on the same module. This goal is achieved by determining the smallest c{\hbox{-}}{\it perfect universal graphs} for data structures "of type X.” Such a graph is the smallest graph that contains a homomorphic image of each n{\hbox{-}}\rm node structure "of type X,” with each node of the image holding \leq c nodes of the structure. In the current paper, "type X” refers to rooted binary trees and three array-like structures: chaotic arrays, ragged arrays, and rectangular arrays. For each of these families of data structures, the number of memory modules needed to achieve conflict tolerance c is determined to within constant factors.

Index Terms:
Parallel memory systems, data structures for parallel systems, bounded-conflict parallel memory access, data mapping, parallel architectures, parallel systems, data structures, graph labeling.
Gennaro Cordasco, Vittorio Scarano, Arnold L. Rosenberg, "Bounded-Collision Memory-Mapping Schemes for Data Structures with Applications to Parallel Memories," IEEE Transactions on Parallel and Distributed Systems, vol. 18, no. 7, pp. 973-982, July 2007, doi:10.1109/TPDS.2007.1024
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