Abstract
We show how to implement divide- and-conquer algorithms without undue overhead on a wide class of networks. We give an optimal generic divide- and-conquer implementation on hypercubes for the class of divide- and-conquer algorithms for which the total size of the subproblems on any level of recursion does not exceed the original problem size. For this implementation, appropriately sized subcubes have to be allocated to the subproblems generated by the divide-step. We take care that these allocation steps do not cause unbalanced distribution of work, and that, asymptotically, they do not increase the running time. Variants of our generic algorithm also work for the butterfly network and, by a general simulation, for the class of hypercubic networks, including the shuffle-exchange and the cube-connected-cycles network. Our results can also be applied to optimally solve various types of routing problems.
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References
M.Y. Chan and S.-J. Lee. Subcube recognition, allocation/deallocation and relocation in hypercubes. Proceedings of the 2nd IEEE Symposium on Parallel and Distributed Processing, 87–93, 1990.
M.-S. Chen and K.G. Shin. Processor allocation in an N-cube multiprocessor using Gray codes. IEEE Transactions on Computers, C-36:1396–1407, 1987.
S. Fortune and J. Wyllie. Parallelism in random access machines. Proceedings of the 10th ACM Symposium on Theory of Computing, 114–118, 1978.
A. van Gelder. PRAM processor allocation: A hidden bottleneck in sublogarithmic algorithms IEEE Transactions on Computers, C-38:289–292, 1989.
J. Kim C.R. Das and W. Lin. A processor allocation scheme for hypercube computers. Proceedings of the 1989 International Conference on Parallel Processing. Vol. 2 Software, 231–238, 1989.
F.T. Leighton. Introduction to Parallel Algorithms and Architectures. Morgan Kaufmann Publishers, 1992.
E.W. Mayr and R. Werchner. Optimal routing of parentheses on the hypercube. Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, 109–117, 1992.
D. Nassimi and S. Sahni. Data broadcasting in SIMD computers. IEEE Transactions on Computers, C-30:101–107, 1981.
D. Nassimi and S. Sahni. A self-routing Benes network and parallel permutation algorithms. IEEE Transactions on Computers, C-31:148–154, 1982.
D. Nassimi and S. Sahni. Parallel permutation and sorting algorithms and a new generalized connection network. JACM, 29:642–667, 1982.
C.G. Plaxton and E.W. Mayr. Pipelined parallel prefix computations and sorting on a pipelined hypercube. Technical Report STAN-CS-89-1269, Stanford University, 1989. To appear in J. Parallel Distrib. Comput.
E.J. Schwabe. On the computational equivalence of hypercube-derived networks. Proceedings of the 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, 388–397, 1990.
J.T. Schwartz. Ultracomputers. ACM Transactions on Programming Languages and Systems, 2:484–521, 1980.
X. Zhong, S. Rajopadhye and V.M. Lo. Parallel implementations of divide-and-conquer algorithms on binary de Bruijn networks. Technical Report CIS-TR-91-21 University of Oregon, 1991.
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© 1993 Springer-Verlag Berlin Heidelberg
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Mayr, E.W., Werchner, R. (1993). Optimal implementation of general divide- and-conquer on the hypercube and related networks. In: Meyer, F., Monien, B., Rosenberg, A.L. (eds) Parallel Architectures and Their Efficient Use. Nixdorf 1992. Lecture Notes in Computer Science, vol 678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56731-3_19
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DOI: https://doi.org/10.1007/3-540-56731-3_19
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