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cPerfect Hashing Schemes for Arrays, with Applications to Parallel Memories
"... We study the problem of mapping arraystructured data to an ensemble of parallel memory modules, by allowing at most c conflicts (i.e. simultaneous access by up to c processors to the same memory module). We seek the smallest ensemble that will allow us to store any nvertex instance of three array ..."
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We study the problem of mapping arraystructured data to an ensemble of parallel memory modules, by allowing at most c conflicts (i.e. simultaneous access by up to c processors to the same memory module). We seek the smallest ensemble that will allow us to store any nvertex instance of three arraylike data structures with no more than c arrayvertices stored on the same module. For the most general family, chaotic arrays, we prove that Θ(n 2 /c 2) memory modules are needed to achieve this bound on conflicts. Similarly tight bounds are found for the other two families, ragged and rectangular arrays. 1
BoundedCollision MemoryMapping Schemes for Data Structures with Applications to Parallel Memories
"... 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 tolerance c, the smalle ..."
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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 tolerance c, the smallest ensemble that allows one to store any nnode 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 cperfect universal graphs for data structures “of type X. ” Such a graph is the smallest graph that contains a homomorphic image of each nnode structure “of type X, ” with each node of the image holding c nodes of the structure. In the current paper, “type X ” refers to rooted binary trees and three arraylike 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, boundedconflict parallel memory access, data mapping, parallel architectures, parallel systems, data structures, graph labeling. Ç