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<p><b>Abstract</b>—Techniques are developed for mapping structured data to an ensemble of parallel memory modules in a way that limits the number of <it>conflicts</it>, i.e., simultaneous accesses by distinct processors to the same memory module. The techniques determine, for any given <it>conflict tolerance</it><tmath>c</tmath>, the smallest ensemble that allows one to store <it>any</it><tmath>n{\hbox{-}}\rm node</tmath> data structure "of type <tmath>X</tmath>” in such a way that no more than <tmath>c</tmath> nodes of a structure are stored on the same module. This goal is achieved by determining the smallest <tmath>c{\hbox{-}}{\it perfect universal graphs}</tmath> for data structures "of type <tmath>X</tmath>.” Such a graph is the smallest graph that contains a homomorphic image of each <tmath>n{\hbox{-}}\rm node</tmath> structure "of type <tmath>X</tmath>,” with each node of the image holding <tmath>\leq c</tmath> nodes of the structure. In the current paper, "type <tmath>X</tmath>” refers to <it>rooted binary trees</it> and three array-like structures: <it>chaotic</it> arrays, <it>ragged</it> arrays, and <it>rectangular</it> arrays. For each of these families of data structures, the number of memory modules needed to achieve conflict tolerance <tmath>c</tmath> is determined to within constant factors.</p>
Parallel memory systems, data structures for parallel systems, bounded-conflict parallel memory access, data mapping, parallel architectures, parallel systems, data structures, graph labeling.
Vittorio Scarano, Arnold L. Rosenberg, Gennaro Cordasco, "Bounded-Collision Memory-Mapping Schemes for Data Structures with Applications to Parallel Memories", IEEE Transactions on Parallel & Distributed Systems, vol. 18, no. , pp. 973-982, July 2007, doi:10.1109/TPDS.2007.1024
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