Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
A Unified theory of interconnection network structure
Theoretical Computer Science
Work-preserving emulations of fixed-connection networks
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Group action graphs and parallel architectures
SIAM Journal on Computing
Embedding mesh of trees in the hypercube
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Embedding meshes of trees into deBruijn graphs
Information Processing Letters
An approach to emulating separable graphs
Proceedings of the 3rd ACM symposium on Parallel algorithms and architectures
Optimal emulations by butterfly-like networks
Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
X-Tree: A tree structured multi-processor computer architecture
ISCA '78 Proceedings of the 5th annual symposium on Computer architecture
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
Efficient embeddings and simulations for hypercubic networks
Efficient embeddings and simulations for hypercubic networks
Parallel Processing with the Perfect Shuffle
IEEE Transactions on Computers
A Comparative Study Of X-Tree, Pyramid And Related Machines
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
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In the theoretical framework of graph embedding and network emulations, we show that the index-shuffle graph (a bounded-degree hypercube-like interconnection network, recently introduced by [ Baumslag and Obrenic (1997): Index-Shuffle Graphs, ...]) efficiently approximates the hypercube in general computations, by emulating the direct-product structure of the hypercube.In the direct product G = G1 脳 G2 脳 ... 脳 Gk let an factor Gi be an instance of any of the three following graphs: cycle, complete binary tree, X - tree. Given an N-node index-shuffle graph 驴n, where N = 2n, and any collection of 2l copies of G, such that: |Gi| 驴 2ni, for i = 1, ... k, where l+ 驴i=1k 驴 and 2驴log2k驴 驴 (max1驴i驴k ni) 驴 n, 驴n emulates any factor Gi, in all copies of G in this collection with slowdown O(log k + log ni) = O(log log N).As a consequence of these and previous results, the index-shuffle graph emerges as a uniqely "universal" bounded-degree hypercube substitute. The index-shuffle graph emulates (multiple copies of) multi-dimensional tori and meshes of trees (or X-trees) with slowdown doubly logarithmic in the size of the graph, which currently cannot be achieved by either butterfiles or shuffles. Furthermore, the butterfly is emulated by its (like-sized) index-shuffle graph with slowdown triply logarithmic in the size ofihe graph, which is currently impossible by shuffles. Finally the index-shuffle graph contains the (equal-sized) shuffle-exchange graph, thus demonstrating communication power not known to be present in the hypercube itself.