Abstract
A deterministic scheme for the simulation of (n, m)-PRAM computation is devised. Each PRAM step is simulated on a bounded degree network consisting of a mesh-of-trees (MT) of siden. The memory is subdivided inn modules, each local to a PRAM processor. The roots of the MT contain these processors and the memory modules, while the otherO(n 2) nodes have the mere capabilities of packet switchers and one-bit comparators. The simulation algorithm makes a crucial use of pipelining on the MT, and attains a time complexity ofO(log2 n/log logn). The best previous time bound wasO(log2 n) on a different interconnection network withn processors. While the previous simulation schemes use an intermediate MPC model, which is in turn simulated on a bounded degree network, our method performs the simulation directly with a simple algorithm.
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References
Fortune, S., and Wyllie, J. Parallelism in Random Access Machines.Proc. 10th ACM STOC, 1978, pp. 114–118.
Schwartz, J. T. Ultracomputers.ACM TOPLAS,2, 1980, pp. 484–521.
Mehlhorn, K., and Vishkin, U. Randomized and deterministic simulations of PRAMs by parallel machines with restricted granularity of parallel memories.Acta Inform.,21, 1984, pp. 339–374.
Alt, H., Hagerup, T., Mehlhorn, K., and Preparata, F. P. Deterministic simulation of idealized parallel computers on more realistic ones.SIAM J. Comput.,16, 1987, pp. 808–835.
Upfal, E., and Wigderson, A. How to share memory in a distributed system.J. Assoc. Comput. Mach.,34, 1987, pp. 116–127.
Upfal, E. A probabilistic relation between desirable and feasible models of parallel computation.Proc. 16th ACM STOC, 1984, pp. 258–265.
Karlin, A. R., and Upfal, E. Parallel hashing—An efficient implementation of shared memory.Proc. 18th ACM STOC, 1986, pp. 160–168.
Ranade, A. G. How to emulate shared memory.Proc. 28th IEEE FOCS, 1987, pp. 185–194.
Luccio, F., Pietracaprina, A., and Pucci, G. An efficient probabilistic simulation of PRAM's in VLSI.Inform. Process. Lett. 28, 1988, pp. 141–147.
Leighton, T. New lower bound techniques for VLSI.Proc. 22nd IEEE FOCS, 1981, pp. 1–12.
Ajtai, M., Komlos, J., and Szemeredi, E. AnO(n logn) sorting network.Proc. 15th ACM STOC, 1983, pp. 1–9.
Leighton, T. Tight bounds on the complexity of parallel sorting.Proc. 16th ACM STOC, 1984, pp. 71–80.
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Communicated by Franco P. Preparata.
This work has been supported in part by Ministero della Pubblica Istruzione of Italy under a research grant.
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Luccio, F., Pietracaprina, A. & Pucci, G. A new scheme for the deterministic simulation of PRAMs in VLSI. Algorithmica 5, 529–544 (1990). https://doi.org/10.1007/BF01840402
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DOI: https://doi.org/10.1007/BF01840402