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Constructive, Deterministic Implementation of Shared Memory on Meshes
| Venue: | SIAM Journal on Computing |
| Citations: | 3 - 3 self |
BibTeX
@ARTICLE{Pietracaprina_constructive,deterministic,
author = {Andrea Pietracaprina and Geppino Pucci and Jop F. Sibeyn},
title = {Constructive, Deterministic Implementation of Shared Memory on Meshes},
journal = {SIAM Journal on Computing},
year = {},
volume = {30},
pages = {2000}
}
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Abstract
This paper describes a scheme to implement a shared address space of size m on an n-node mesh, with m polynomial in n, where each mesh node hosts a processor and a memory module. At the core of the simulation is a Hierarchical Memory Organization Scheme (HMOS), which governs the distribution of the shared variables, each replicated into multiple copies, among the memory modules, through a cascade of bipartite graphs. Based on the expansion properties of such graphs, we devise a protocol that accesses any n-tuple of shared variables in worst-case time O \Gamma n 1=2+j \Delta , for any constant j ? 0, using O \Gamma 1=j 1:59 \Delta copies per variable, or in worst-case time O \Gamma n 1=2 log n \Delta , using O \Gamma log 1:59 n \Delta copies per variable. In both cases the access time is close to the natural O ( p n) lower bound imposed by the network diameter. A key feature of the scheme is that it can be made fully constructive when m is not too large, t...
